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443 lines
994 KiB
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443 lines
994 KiB
Markdown
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<!--
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<pre class="Agda"><a id="14" class="Keyword">open</a> <a id="19" class="Keyword">import</a> <a id="26" href="Level.html" class="Module">Level</a>
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<a id="32" class="Keyword">open</a> <a id="37" class="Keyword">import</a> <a id="44" href="Category.Ambient.html" class="Module">Category.Ambient</a> <a id="61" class="Keyword">using</a> <a id="67" class="Symbol">(</a><a id="68" href="Category.Ambient.html#1681" class="Record">Ambient</a><a id="75" class="Symbol">)</a>
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<a id="77" class="Keyword">open</a> <a id="82" class="Keyword">import</a> <a id="89" href="Categories.Monad.Commutative.html" class="Module">Categories.Monad.Commutative</a>
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<a id="118" class="Keyword">open</a> <a id="123" class="Keyword">import</a> <a id="130" href="Categories.Monad.Strong.html" class="Module">Categories.Monad.Strong</a>
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<a id="154" class="Keyword">open</a> <a id="159" class="Keyword">import</a> <a id="166" href="Data.Product.html" class="Module">Data.Product</a> <a id="179" class="Keyword">using</a> <a id="185" class="Symbol">(</a><a id="186" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">_,_</a><a id="189" class="Symbol">)</a> <a id="191" class="Keyword">renaming</a> <a id="200" class="Symbol">(</a><a id="201" href="Data.Product.Base.html#1618" class="Function Operator">_×_</a> <a id="205" class="Symbol">to</a> <a id="208" class="Function Operator">_×f_</a><a id="212" class="Symbol">)</a>
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<a id="214" class="Keyword">open</a> <a id="219" class="Keyword">import</a> <a id="226" href="Categories.FreeObjects.Free.html" class="Module">Categories.FreeObjects.Free</a>
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<a id="254" class="Keyword">import</a> <a id="261" href="Monad.Instance.K.html" class="Module">Monad.Instance.K</a> <a id="278" class="Symbol">as</a> <a id="281" class="Module">MIK</a>
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<a id="285" class="Keyword">open</a> <a id="290" class="Keyword">import</a> <a id="297" href="Categories.Morphism.Properties.html" class="Module">Categories.Morphism.Properties</a>
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</pre>-->
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<pre class="Agda"><a id="345" class="Keyword">module</a> <a id="352" href="Monad.Instance.K.Commutative.html" class="Module">Monad.Instance.K.Commutative</a> <a id="381" class="Symbol">{</a><a id="382" href="Monad.Instance.K.Commutative.html#382" class="Bound">o</a> <a id="384" href="Monad.Instance.K.Commutative.html#384" class="Bound">ℓ</a> <a id="386" href="Monad.Instance.K.Commutative.html#386" class="Bound">e</a><a id="387" class="Symbol">}</a> <a id="389" class="Symbol">(</a><a id="390" href="Monad.Instance.K.Commutative.html#390" class="Bound">ambient</a> <a id="398" class="Symbol">:</a> <a id="400" href="Category.Ambient.html#1681" class="Record">Ambient</a> <a id="408" href="Monad.Instance.K.Commutative.html#382" class="Bound">o</a> <a id="410" href="Monad.Instance.K.Commutative.html#384" class="Bound">ℓ</a> <a id="412" href="Monad.Instance.K.Commutative.html#386" class="Bound">e</a><a id="413" class="Symbol">)</a> <a id="415" class="Symbol">(</a><a id="416" href="Monad.Instance.K.Commutative.html#416" class="Bound">MK</a> <a id="419" class="Symbol">:</a> <a id="421" href="Monad.Instance.K.html#1123" class="Record">MIK.MonadK</a> <a id="432" href="Monad.Instance.K.Commutative.html#390" class="Bound">ambient</a><a id="439" class="Symbol">)</a> <a id="441" class="Keyword">where</a>
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<a id="447" class="Keyword">open</a> <a id="452" href="Category.Ambient.html#1681" class="Module">Ambient</a> <a id="460" href="Monad.Instance.K.Commutative.html#390" class="Bound">ambient</a>
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<a id="468" class="Keyword">open</a> <a id="473" href="Monad.Instance.K.html" class="Module">MIK</a> <a id="477" href="Monad.Instance.K.Commutative.html#390" class="Bound">ambient</a>
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<a id="485" class="Keyword">open</a> <a id="490" href="Monad.Instance.K.html#1123" class="Module">MonadK</a> <a id="497" href="Monad.Instance.K.Commutative.html#416" class="Bound">MK</a>
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<a id="500" class="Keyword">open</a> <a id="505" class="Keyword">import</a> <a id="512" href="Monad.Instance.K.Strong.html" class="Module">Monad.Instance.K.Strong</a> <a id="536" href="Monad.Instance.K.Commutative.html#390" class="Bound">ambient</a> <a id="544" href="Monad.Instance.K.Commutative.html#416" class="Bound">MK</a>
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<a id="547" class="Keyword">open</a> <a id="552" class="Keyword">import</a> <a id="559" href="Monad.Instance.K.EquationalLifting.html" class="Module">Monad.Instance.K.EquationalLifting</a> <a id="594" href="Monad.Instance.K.Commutative.html#390" class="Bound">ambient</a> <a id="602" href="Monad.Instance.K.Commutative.html#416" class="Bound">MK</a>
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<a id="605" class="Keyword">open</a> <a id="610" class="Keyword">import</a> <a id="617" href="Category.Construction.ElgotAlgebras.html" class="Module">Category.Construction.ElgotAlgebras</a> <a id="653" href="Categories.Category.Extensive.html#734" class="Function">cocartesian</a>
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<a id="665" class="Keyword">open</a> <a id="670" class="Keyword">import</a> <a id="677" href="Algebra.Elgot.html" class="Module">Algebra.Elgot</a> <a id="691" href="Categories.Category.Extensive.html#734" class="Function">cocartesian</a>
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<a id="703" class="Keyword">open</a> <a id="708" class="Keyword">import</a> <a id="715" href="Algebra.Elgot.Free.html" class="Module">Algebra.Elgot.Free</a> <a id="734" href="Categories.Category.Extensive.html#734" class="Function">cocartesian</a> <a id="746" class="Keyword">using</a> <a id="752" class="Symbol">(</a><a id="753" href="Algebra.Elgot.Free.html#1441" class="Function">FreeElgotAlgebra</a><a id="769" class="Symbol">;</a> <a id="771" href="Algebra.Elgot.Free.html#1197" class="Function">elgotForgetfulF</a><a id="786" class="Symbol">)</a>
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<a id="788" class="Keyword">open</a> <a id="793" class="Keyword">import</a> <a id="800" href="Algebra.Elgot.Stable.html" class="Module">Algebra.Elgot.Stable</a> <a id="821" href="Category.Ambient.html#2762" class="Function">distributive</a> <a id="834" class="Keyword">using</a> <a id="840" class="Symbol">(</a><a id="841" href="Algebra.Elgot.Stable.html#2437" class="Record">IsStableFreeElgotAlgebra</a><a id="865" class="Symbol">;</a> <a id="867" href="Algebra.Elgot.Stable.html#1438" class="Record">IsStableFreeElgotAlgebraˡ</a><a id="892" class="Symbol">;</a> <a id="894" href="Algebra.Elgot.Stable.html#3436" class="Function">isStable⇒isStableˡ</a><a id="912" class="Symbol">)</a>
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<a id="915" class="Keyword">open</a> <a id="920" href="Categories.Category.Core.html#1530" class="Module">Equiv</a>
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<a id="926" class="Keyword">open</a> <a id="931" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
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<a id="944" class="Keyword">open</a> <a id="949" href="Category.Ambient.html#9087" class="Module">MR</a> <a id="952" href="Category.Ambient.html#1757" class="Function">C</a>
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<a id="954" class="Keyword">open</a> <a id="959" href="Category.Ambient.html#9069" class="Module">M</a> <a id="961" href="Category.Ambient.html#1757" class="Function">C</a>
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</pre>
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# K is a commutative monad
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The proof is analogous to the ones for strength, the relevant diagram is:
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<iframe class="quiver-embed" src="https://q.uiver.app/#q=WzAsNyxbMCwxLCJLWCBcXHRpbWVzIEtZIl0sWzEsMCwiSyhLWCBcXHRpbWVzIFkpIl0sWzIsMCwiSyhLKFggXFx0aW1lcyBZKSkiXSxbMywxLCJLKFggXFx0aW1lcyBZKSJdLFsxLDIsIksoWCBcXHRpbWVzIEtZKSJdLFsyLDIsIksoSyhYIFxcdGltZXMgWSkpIl0sWzAsNCwiS1ggXFx0aW1lcyBZIl0sWzAsMSwiXFx0YXUiXSxbMSwyLCJLXFxoYXR7XFx0YXV9Il0sWzIsMywiXFxtdSJdLFswLDQsIlxcaGF0e1xcdGF1fSIsMl0sWzQsNSwiS1xcdGF1IiwyXSxbNSwzLCJcXG11IiwyXSxbNiwwLCJpZCBcXHRpbWVzIFxcZXRhIl0sWzYsMywiXFxoYXR7XFx0YXV9IiwwLHsiY3VydmUiOjV9XSxbMCwzLCJcXGhhdHtcXHRhdX1eXFwjIl1d&embed" width="974" height="688" style="border-radius: 8px; border: none;"></iframe>
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<pre class="Agda">
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<a id="2215" class="Keyword">open</a> <a id="2220" href="Monad.Instance.K.html#1672" class="Module">monadK</a> <a id="2227" class="Keyword">using</a> <a id="2233" class="Symbol">(</a><a id="2234" href="Categories.Monad.html#583" class="Function">μ</a><a id="2235" class="Symbol">)</a>
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<a id="2237" class="Keyword">open</a> <a id="2242" href="Monad.Instance.K.html#1775" class="Module">kleisliK</a> <a id="2251" class="Keyword">using</a> <a id="2257" class="Symbol">(</a><a id="2258" href="Categories.Monad.Relative.html#895" class="Function">extend</a><a id="2264" class="Symbol">)</a>
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<a id="2266" class="Keyword">open</a> <a id="2271" href="Monad.Instance.K.Strong.html#22135" class="Module">strongK</a> <a id="2279" class="Keyword">using</a> <a id="2285" class="Symbol">(</a><a id="2286" href="Categories.Monad.Strong.html#1060" class="Function">strengthen</a><a id="2296" class="Symbol">)</a>
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<a id="2298" class="Keyword">open</a> <a id="2303" href="Algebra.Elgot.Stable.html#2437" class="Module">IsStableFreeElgotAlgebra</a> <a id="2328" class="Keyword">using</a> <a id="2334" class="Symbol">(</a><a id="2335" href="Algebra.Elgot.Stable.html#2784" class="Field">♯-law</a><a id="2340" class="Symbol">;</a> <a id="2342" href="Algebra.Elgot.Stable.html#2892" class="Field">♯-preserving</a><a id="2354" class="Symbol">;</a> <a id="2356" href="Algebra.Elgot.Stable.html#3117" class="Field">♯-unique</a><a id="2364" class="Symbol">)</a>
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<a id="2366" class="Keyword">open</a> <a id="2371" href="Algebra.Elgot.Stable.html#1438" class="Module">IsStableFreeElgotAlgebraˡ</a> <a id="2397" class="Keyword">using</a> <a id="2403" class="Symbol">(</a><a id="2404" href="Algebra.Elgot.Stable.html#2117" class="Field">♯ˡ-unique</a><a id="2413" class="Symbol">;</a> <a id="2415" href="Algebra.Elgot.Stable.html#1891" class="Field">♯ˡ-preserving</a><a id="2428" class="Symbol">;</a> <a id="2430" href="Algebra.Elgot.Stable.html#1783" class="Field">♯ˡ-law</a><a id="2436" class="Symbol">)</a>
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<a id="2438" class="Keyword">open</a> <a id="2443" href="Algebra.Elgot.html#15964" class="Module">Elgot-Algebra</a> <a id="2457" class="Keyword">using</a> <a id="2463" class="Symbol">(</a><a id="2464" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a><a id="2476" class="Symbol">;</a> <a id="2478" href="Algebra.Elgot.html#2011" class="Function">#-Fixpoint</a><a id="2488" class="Symbol">;</a> <a id="2490" href="Algebra.Elgot.html#2470" class="Function">#-Compositionality</a><a id="2508" class="Symbol">;</a> <a id="2510" href="Algebra.Elgot.html#8386" class="Function">#-Diamond</a><a id="2519" class="Symbol">;</a> <a id="2521" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a><a id="2529" class="Symbol">)</a>
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<a id="2534" class="Comment">-- some helper definitions to make our life easier</a>
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<a id="2585" class="Keyword">private</a>
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<a id="stableˡ"></a><a id="2595" href="Monad.Instance.K.Commutative.html#2595" class="Function">stableˡ</a> <a id="2603" class="Symbol">=</a> <a id="2605" class="Symbol">λ</a> <a id="2607" href="Monad.Instance.K.Commutative.html#2607" class="Bound">X</a> <a id="2609" class="Symbol">→</a> <a id="2611" href="Algebra.Elgot.Stable.html#3436" class="Function">isStable⇒isStableˡ</a> <a id="2630" class="Symbol">(</a><a id="2631" href="Monad.Instance.K.html#1182" class="Field">freealgebras</a> <a id="2644" href="Monad.Instance.K.Commutative.html#2607" class="Bound">X</a><a id="2645" class="Symbol">)</a> <a id="2647" class="Symbol">(</a><a id="2648" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="2655" href="Monad.Instance.K.Commutative.html#2607" class="Bound">X</a><a id="2656" class="Symbol">)</a>
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<a id="η"></a><a id="2660" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="2662" class="Symbol">=</a> <a id="2664" class="Symbol">λ</a> <a id="2666" href="Monad.Instance.K.Commutative.html#2666" class="Bound">Z</a> <a id="2668" class="Symbol">→</a> <a id="2670" href="Categories.FreeObjects.Free.html#854" class="Field">FreeObject.η</a> <a id="2683" class="Symbol">(</a><a id="2684" href="Monad.Instance.K.html#1182" class="Field">freealgebras</a> <a id="2697" href="Monad.Instance.K.Commutative.html#2666" class="Bound">Z</a><a id="2698" class="Symbol">)</a>
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<a id="_♯"></a><a id="2702" href="Monad.Instance.K.Commutative.html#2702" class="Function Operator">_♯</a> <a id="2705" class="Symbol">=</a> <a id="2707" class="Symbol">λ</a> <a id="2709" class="Symbol">{</a><a id="2710" href="Monad.Instance.K.Commutative.html#2710" class="Bound">A</a> <a id="2712" href="Monad.Instance.K.Commutative.html#2712" class="Bound">X</a> <a id="2714" href="Monad.Instance.K.Commutative.html#2714" class="Bound">Y</a><a id="2715" class="Symbol">}</a> <a id="2717" href="Monad.Instance.K.Commutative.html#2717" class="Bound">f</a> <a id="2719" class="Symbol">→</a> <a id="2721" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">IsStableFreeElgotAlgebra.[_,_]♯</a> <a id="2753" class="Symbol">{</a><a id="2754" class="Argument">Y</a> <a id="2756" class="Symbol">=</a> <a id="2758" href="Monad.Instance.K.Commutative.html#2712" class="Bound">X</a><a id="2759" class="Symbol">}</a> <a id="2761" class="Symbol">(</a><a id="2762" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="2769" href="Monad.Instance.K.Commutative.html#2712" class="Bound">X</a><a id="2770" class="Symbol">)</a> <a id="2772" class="Symbol">{</a><a id="2773" class="Argument">X</a> <a id="2775" class="Symbol">=</a> <a id="2777" href="Monad.Instance.K.Commutative.html#2710" class="Bound">A</a><a id="2778" class="Symbol">}</a> <a id="2780" class="Symbol">(</a><a id="2781" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="2790" href="Monad.Instance.K.Commutative.html#2714" class="Bound">Y</a><a id="2791" class="Symbol">)</a> <a id="2793" href="Monad.Instance.K.Commutative.html#2717" class="Bound">f</a>
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<a id="_♯ˡ"></a><a id="2797" href="Monad.Instance.K.Commutative.html#2797" class="Function Operator">_♯ˡ</a> <a id="2801" class="Symbol">=</a> <a id="2803" class="Symbol">λ</a> <a id="2805" class="Symbol">{</a><a id="2806" href="Monad.Instance.K.Commutative.html#2806" class="Bound">A</a> <a id="2808" href="Monad.Instance.K.Commutative.html#2808" class="Bound">X</a> <a id="2810" href="Monad.Instance.K.Commutative.html#2810" class="Bound">Y</a><a id="2811" class="Symbol">}</a> <a id="2813" href="Monad.Instance.K.Commutative.html#2813" class="Bound">f</a> <a id="2815" class="Symbol">→</a> <a id="2817" href="Algebra.Elgot.Stable.html#1658" class="Field Operator">IsStableFreeElgotAlgebraˡ.[_,_]♯ˡ</a> <a id="2851" class="Symbol">{</a><a id="2852" class="Argument">Y</a> <a id="2854" class="Symbol">=</a> <a id="2856" href="Monad.Instance.K.Commutative.html#2808" class="Bound">X</a><a id="2857" class="Symbol">}</a> <a id="2859" class="Symbol">(</a><a id="2860" href="Monad.Instance.K.Commutative.html#2595" class="Function">stableˡ</a> <a id="2868" href="Monad.Instance.K.Commutative.html#2808" class="Bound">X</a><a id="2869" class="Symbol">)</a> <a id="2871" class="Symbol">{</a><a id="2872" class="Argument">X</a> <a id="2874" class="Symbol">=</a> <a id="2876" href="Monad.Instance.K.Commutative.html#2806" class="Bound">A</a><a id="2877" class="Symbol">}</a> <a id="2879" class="Symbol">(</a><a id="2880" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="2889" href="Monad.Instance.K.Commutative.html#2810" class="Bound">Y</a><a id="2890" class="Symbol">)</a> <a id="2892" href="Monad.Instance.K.Commutative.html#2813" class="Bound">f</a>
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<a id="_#"></a><a id="2896" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">_#</a> <a id="2899" class="Symbol">=</a> <a id="2901" class="Symbol">λ</a> <a id="2903" class="Symbol">{</a><a id="2904" href="Monad.Instance.K.Commutative.html#2904" class="Bound">A</a><a id="2905" class="Symbol">}</a> <a id="2907" class="Symbol">{</a><a id="2908" href="Monad.Instance.K.Commutative.html#2908" class="Bound">X</a><a id="2909" class="Symbol">}</a> <a id="2911" href="Monad.Instance.K.Commutative.html#2911" class="Bound">f</a> <a id="2913" class="Symbol">→</a> <a id="2915" href="Algebra.Elgot.html#1938" class="Function Operator">Elgot-Algebra._#</a> <a id="2932" class="Symbol">(</a><a id="2933" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="2942" href="Monad.Instance.K.Commutative.html#2904" class="Bound">A</a><a id="2943" class="Symbol">)</a> <a id="2945" class="Symbol">{</a><a id="2946" class="Argument">X</a> <a id="2948" class="Symbol">=</a> <a id="2950" href="Monad.Instance.K.Commutative.html#2908" class="Bound">X</a><a id="2951" class="Symbol">}</a> <a id="2953" href="Monad.Instance.K.Commutative.html#2911" class="Bound">f</a>
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<a id="2956" class="Comment">-- First we establish some facts about σ</a>
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<a id="σ"></a><a id="2998" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="3000" class="Symbol">:</a> <a id="3002" class="Symbol">∀</a> <a id="3004" class="Symbol">(</a><a id="3005" href="Monad.Instance.K.Commutative.html#3005" class="Bound">(</a><a id="3006" href="Monad.Instance.K.Commutative.html#3006" class="Bound">X</a> <a id="3008" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="3010" href="Monad.Instance.K.Commutative.html#3010" class="Bound">Y</a><a id="3011" href="Monad.Instance.K.Commutative.html#3005" class="Bound">)</a> <a id="3013" class="Symbol">:</a> <a id="3015" href="Categories.Category.Core.html#559" class="Function">Obj</a> <a id="3019" href="Monad.Instance.K.Commutative.html#208" class="Function Operator">×f</a> <a id="3022" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="3025" class="Symbol">)</a> <a id="3027" class="Symbol">→</a> <a id="3029" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="3033" href="Monad.Instance.K.Commutative.html#3006" class="Bound">X</a> <a id="3035" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="3037" href="Monad.Instance.K.Commutative.html#3010" class="Bound">Y</a> <a id="3039" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3041" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="3045" class="Symbol">(</a><a id="3046" href="Monad.Instance.K.Commutative.html#3006" class="Bound">X</a> <a id="3048" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="3050" href="Monad.Instance.K.Commutative.html#3010" class="Bound">Y</a><a id="3051" class="Symbol">)</a>
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<a id="3053" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="3055" class="Symbol">_</a> <a id="3057" class="Symbol">=</a> <a id="3059" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3063" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3068" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3070" class="Symbol">(</a><a id="3071" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="3073" class="Symbol">_)</a> <a id="3076" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3078" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a>
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<a id="σ-η"></a><a id="3084" href="Monad.Instance.K.Commutative.html#3084" class="Function">σ-η</a> <a id="3088" class="Symbol">:</a> <a id="3090" class="Symbol">∀</a> <a id="3092" class="Symbol">{</a><a id="3093" href="Monad.Instance.K.Commutative.html#3093" class="Bound">X</a> <a id="3095" href="Monad.Instance.K.Commutative.html#3095" class="Bound">Y</a><a id="3096" class="Symbol">}</a> <a id="3098" class="Symbol">→</a> <a id="3100" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="3102" class="Symbol">(</a><a id="3103" href="Monad.Instance.K.Commutative.html#3093" class="Bound">X</a> <a id="3105" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="3107" href="Monad.Instance.K.Commutative.html#3095" class="Bound">Y</a><a id="3108" class="Symbol">)</a> <a id="3110" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3112" class="Symbol">(</a><a id="3113" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="3115" class="Symbol">_</a> <a id="3117" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3119" href="Category.Ambient.html#2115" class="Function">idC</a><a id="3122" class="Symbol">)</a> <a id="3124" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3126" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="3128" class="Symbol">_</a>
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<a id="3130" href="Monad.Instance.K.Commutative.html#3084" class="Function">σ-η</a> <a id="3134" class="Symbol">=</a> <a id="3136" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="3144" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="3146" class="Symbol">(_</a> <a id="3149" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="3151" class="Symbol">_)</a> <a id="3154" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3156" class="Symbol">(</a><a id="3157" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="3159" class="Symbol">_</a> <a id="3161" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3163" href="Category.Ambient.html#2115" class="Function">idC</a><a id="3166" class="Symbol">)</a> <a id="3186" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3189" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="3195" class="Symbol">(</a><a id="3196" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="3202" href="Categories.Category.BinaryProducts.html#4512" class="Function">swap∘⁂</a><a id="3208" class="Symbol">)</a> <a id="3210" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="3214" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3218" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3223" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3225" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="3227" class="Symbol">(_</a> <a id="3230" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="3232" class="Symbol">_)</a> <a id="3235" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3237" class="Symbol">(</a><a id="3238" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="3242" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3244" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="3246" class="Symbol">_)</a> <a id="3249" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3251" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3256" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3259" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="3267" class="Symbol">(</a><a id="3268" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="3274" class="Symbol">(</a><a id="3275" href="Monad.Instance.K.Strong.html#3312" class="Function">τ-η</a> <a id="3279" class="Symbol">_))</a> <a id="3283" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="3289" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3293" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3298" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3300" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="3302" class="Symbol">_</a> <a id="3304" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3306" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3329" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3332" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="3338" class="Symbol">(</a><a id="3339" href="Monad.Instance.K.Strong.html#5746" class="Function">K₁η</a> <a id="3343" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="3347" class="Symbol">)</a> <a id="3349" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="3353" class="Symbol">(</a><a id="3354" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="3356" class="Symbol">_</a> <a id="3358" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3360" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="3364" class="Symbol">)</a> <a id="3366" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3368" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3395" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3398" href="Categories.Morphism.Reasoning.Core.html#6665" class="Function">cancelʳ</a> <a id="3406" href="Categories.Category.BinaryProducts.html#4688" class="Function">swap∘swap</a> <a id="3416" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="3420" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="3422" class="Symbol">(_</a> <a id="3425" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="3427" class="Symbol">_)</a> <a id="3462" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="σ-comm"></a><a id="3465" href="Monad.Instance.K.Commutative.html#3465" class="Function">σ-comm</a> <a id="3472" class="Symbol">:</a> <a id="3474" class="Symbol">∀</a> <a id="3476" class="Symbol">{</a><a id="3477" href="Monad.Instance.K.Commutative.html#3477" class="Bound">X</a> <a id="3479" href="Monad.Instance.K.Commutative.html#3479" class="Bound">Y</a> <a id="3481" href="Monad.Instance.K.Commutative.html#3481" class="Bound">Z</a><a id="3482" class="Symbol">}</a> <a id="3484" class="Symbol">(</a><a id="3485" href="Monad.Instance.K.Commutative.html#3485" class="Bound">h</a> <a id="3487" class="Symbol">:</a> <a id="3489" href="Monad.Instance.K.Commutative.html#3481" class="Bound">Z</a> <a id="3491" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3493" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="3497" href="Monad.Instance.K.Commutative.html#3477" class="Bound">X</a> <a id="3499" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="3501" href="Monad.Instance.K.Commutative.html#3481" class="Bound">Z</a><a id="3502" class="Symbol">)</a> <a id="3504" class="Symbol">→</a> <a id="3506" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="3508" class="Symbol">(</a><a id="3509" href="Monad.Instance.K.Commutative.html#3477" class="Bound">X</a> <a id="3511" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="3513" href="Monad.Instance.K.Commutative.html#3479" class="Bound">Y</a><a id="3514" class="Symbol">)</a> <a id="3516" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3518" class="Symbol">(</a><a id="3519" href="Monad.Instance.K.Commutative.html#3485" class="Bound">h</a> <a id="3521" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="3523" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3525" href="Category.Ambient.html#2115" class="Function">idC</a><a id="3528" class="Symbol">)</a> <a id="3530" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3532" class="Symbol">((</a><a id="3534" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="3536" class="Symbol">_</a> <a id="3538" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="3541" href="Category.Ambient.html#2115" class="Function">idC</a><a id="3544" class="Symbol">)</a> <a id="3546" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3548" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="3562" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3564" class="Symbol">(</a><a id="3565" href="Monad.Instance.K.Commutative.html#3485" class="Bound">h</a> <a id="3567" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3569" href="Category.Ambient.html#2115" class="Function">idC</a><a id="3572" class="Symbol">))</a><a id="3574" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
|
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<a id="3576" href="Monad.Instance.K.Commutative.html#3465" class="Function">σ-comm</a> <a id="3583" class="Symbol">{</a><a id="3584" href="Monad.Instance.K.Commutative.html#3584" class="Bound">X</a><a id="3585" class="Symbol">}</a> <a id="3587" class="Symbol">{</a><a id="3588" href="Monad.Instance.K.Commutative.html#3588" class="Bound">Y</a><a id="3589" class="Symbol">}</a> <a id="3591" class="Symbol">{</a><a id="3592" href="Monad.Instance.K.Commutative.html#3592" class="Bound">Z</a><a id="3593" class="Symbol">}</a> <a id="3595" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a> <a id="3597" class="Symbol">=</a> <a id="3599" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
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<a id="3607" class="Symbol">(</a><a id="3608" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3612" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3617" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3619" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="3621" class="Symbol">_</a> <a id="3623" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3625" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="3629" class="Symbol">)</a> <a id="3631" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3633" class="Symbol">(</a><a id="3634" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a> <a id="3636" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="3638" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3640" href="Category.Ambient.html#2115" class="Function">idC</a><a id="3643" class="Symbol">)</a> <a id="3685" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3688" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="3694" class="Symbol">(</a><a id="3695" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="3701" href="Categories.Category.BinaryProducts.html#4512" class="Function">swap∘⁂</a><a id="3707" class="Symbol">)</a> <a id="3709" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
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<a id="3713" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3717" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3722" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3724" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="3726" class="Symbol">_</a> <a id="3728" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3730" class="Symbol">(</a><a id="3731" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="3735" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3737" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a> <a id="3739" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="3740" class="Symbol">)</a> <a id="3742" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3744" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3791" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3794" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="3802" class="Symbol">(</a><a id="3803" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="3809" class="Symbol">(</a><a id="3810" href="Monad.Instance.K.Strong.html#5557" class="Function">τ-comm</a> <a id="3817" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a><a id="3818" class="Symbol">))</a> <a id="3821" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="3825" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3829" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3834" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3836" class="Symbol">((</a><a id="3838" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="3840" class="Symbol">_</a> <a id="3842" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="3845" href="Category.Ambient.html#2115" class="Function">idC</a><a id="3848" class="Symbol">)</a> <a id="3850" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3852" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="3866" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3868" class="Symbol">(</a><a id="3869" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="3873" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3875" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a><a id="3876" class="Symbol">))</a> <a id="3879" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="3881" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3883" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="3903" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3906" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="3912" class="Symbol">(</a><a id="3913" href="Category.Construction.ElgotAlgebras.html#812" class="Field">Elgot-Algebra-Morphism.preserves</a> <a id="3946" class="Symbol">(((</a><a id="3949" href="Monad.Instance.K.html#1182" class="Field">freealgebras</a> <a id="3962" class="Symbol">_)</a> <a id="3965" href="Categories.FreeObjects.Free.html#880" class="Field Operator">FreeObject.*</a><a id="3977" class="Symbol">)</a> <a id="3979" class="Symbol">(</a><a id="3980" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="3982" class="Symbol">_</a> <a id="3984" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3986" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="3990" class="Symbol">)))</a> <a id="3994" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="3998" class="Symbol">((</a><a id="4000" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="4004" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4009" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4012" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4015" class="Symbol">)</a> <a id="4017" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4019" class="Symbol">(</a><a id="4020" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="4022" class="Symbol">(</a><a id="4023" href="Monad.Instance.K.Commutative.html#3588" class="Bound">Y</a> <a id="4025" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="4027" href="Monad.Instance.K.Commutative.html#3584" class="Bound">X</a><a id="4028" class="Symbol">)</a> <a id="4030" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4033" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4036" class="Symbol">)</a> <a id="4038" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4040" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="4054" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4056" class="Symbol">(</a><a id="4057" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="4061" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4063" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a><a id="4064" class="Symbol">))</a> <a id="4067" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="4069" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4071" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4076" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="4079" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="4083" class="Symbol">(</a><a id="4084" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a> <a id="4097" class="Symbol">(</a><a id="4098" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="4107" class="Symbol">_)</a> <a id="4110" class="Symbol">(</a><a id="4111" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="4115" href="Monad.Instance.K.Commutative.html#4220" class="Function">by-uni</a><a id="4121" class="Symbol">))</a> <a id="4124" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="4128" class="Symbol">((</a><a id="4130" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="4132" class="Symbol">(</a><a id="4133" href="Monad.Instance.K.Commutative.html#3584" class="Bound">X</a> <a id="4135" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="4137" href="Monad.Instance.K.Commutative.html#3588" class="Bound">Y</a><a id="4138" class="Symbol">)</a> <a id="4140" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4143" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4146" class="Symbol">)</a> <a id="4148" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4150" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="4164" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4166" class="Symbol">(</a><a id="4167" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a> <a id="4169" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4171" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4174" class="Symbol">))</a> <a id="4177" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="4206" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="4210" class="Keyword">where</a>
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<a id="4220" href="Monad.Instance.K.Commutative.html#4220" class="Function">by-uni</a> <a id="4227" class="Symbol">:</a> <a id="4229" class="Symbol">((</a><a id="4231" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="4235" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4240" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4243" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4246" class="Symbol">)</a> <a id="4248" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4250" class="Symbol">(</a><a id="4251" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="4253" class="Symbol">_</a> <a id="4255" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4258" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4261" class="Symbol">)</a> <a id="4263" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4265" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="4279" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4281" class="Symbol">(</a><a id="4282" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="4286" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4288" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a><a id="4289" class="Symbol">))</a> <a id="4292" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4294" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4299" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="4301" class="Symbol">(</a><a id="4302" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="4306" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4309" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="4313" class="Symbol">)</a> <a id="4315" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4317" class="Symbol">(</a><a id="4318" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="4320" class="Symbol">(</a><a id="4321" href="Monad.Instance.K.Commutative.html#3584" class="Bound">X</a> <a id="4323" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="4325" href="Monad.Instance.K.Commutative.html#3588" class="Bound">Y</a><a id="4326" class="Symbol">)</a> <a id="4328" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4331" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4334" class="Symbol">)</a> <a id="4336" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4338" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="4352" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4354" class="Symbol">(</a><a id="4355" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a> <a id="4357" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4359" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4362" class="Symbol">)</a>
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<a id="4368" href="Monad.Instance.K.Commutative.html#4220" class="Function">by-uni</a> <a id="4375" class="Symbol">=</a> <a id="4377" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="4389" class="Symbol">((</a><a id="4391" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="4395" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4400" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4403" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4406" class="Symbol">)</a> <a id="4408" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4410" class="Symbol">(</a><a id="4411" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="4413" class="Symbol">_</a> <a id="4415" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4418" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4421" class="Symbol">)</a> <a id="4423" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4425" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="4439" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4441" class="Symbol">(</a><a id="4442" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="4446" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4448" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a><a id="4449" class="Symbol">))</a> <a id="4452" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4454" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4475" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="4478" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="4484" class="Symbol">(</a><a id="4485" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="4491" class="Symbol">(</a><a id="4492" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="4498" class="Symbol">(</a><a id="4499" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="4503" href="Categories.Category.BinaryProducts.html#4512" class="Function">swap∘⁂</a><a id="4509" class="Symbol">)))</a> <a id="4513" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="4521" class="Symbol">(</a><a id="4522" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="4526" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4531" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4534" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4537" class="Symbol">)</a> <a id="4539" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4541" class="Symbol">(</a><a id="4542" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="4544" class="Symbol">(</a><a id="4545" href="Monad.Instance.K.Commutative.html#3588" class="Bound">Y</a> <a id="4547" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="4549" href="Monad.Instance.K.Commutative.html#3584" class="Bound">X</a><a id="4550" class="Symbol">)</a> <a id="4552" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4555" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4558" class="Symbol">)</a> <a id="4560" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4562" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="4576" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4578" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4583" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4585" class="Symbol">(</a><a id="4586" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a> <a id="4588" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4590" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4593" class="Symbol">)</a> <a id="4607" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="4610" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="4618" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="4626" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="4632" href="Categories.Category.Distributive.Properties.html#5762" class="Function">distributeˡ⁻¹∘swap</a> <a id="4651" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="4659" class="Symbol">(</a><a id="4660" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="4664" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4669" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4672" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4675" class="Symbol">)</a> <a id="4677" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4679" class="Symbol">(</a><a id="4680" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="4682" class="Symbol">(</a><a id="4683" href="Monad.Instance.K.Commutative.html#3588" class="Bound">Y</a> <a id="4685" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="4687" href="Monad.Instance.K.Commutative.html#3584" class="Bound">X</a><a id="4688" class="Symbol">)</a> <a id="4690" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4693" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4696" class="Symbol">)</a> <a id="4698" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4700" class="Symbol">((</a><a id="4702" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4707" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4710" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="4714" class="Symbol">)</a> <a id="4716" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4718" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a><a id="4731" class="Symbol">)</a> <a id="4733" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4735" class="Symbol">(</a><a id="4736" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a> <a id="4738" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4740" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4743" class="Symbol">)</a> <a id="4745" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="4748" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="4754" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="4760" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="4768" class="Symbol">(</a><a id="4769" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="4773" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4778" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4780" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="4782" class="Symbol">_</a> <a id="4784" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4787" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="4791" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4793" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4796" class="Symbol">)</a> <a id="4798" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4800" class="Symbol">((</a><a id="4802" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="4807" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4810" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="4814" class="Symbol">)</a> <a id="4816" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4818" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a><a id="4831" class="Symbol">)</a> <a id="4833" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4835" class="Symbol">(</a><a id="4836" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a> <a id="4838" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4840" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4843" class="Symbol">)</a> <a id="4854" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="4857" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="4863" class="Symbol">(</a><a id="4864" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="4870" class="Symbol">(</a><a id="4871" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="4877" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="4879" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="4888" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="4894" class="Symbol">(</a><a id="4895" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="4901" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="4910" class="Symbol">)))</a> <a id="4914" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="4922" class="Symbol">((</a><a id="4924" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="4926" class="Symbol">_</a> <a id="4928" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4931" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="4935" class="Symbol">)</a> <a id="4937" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4939" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a><a id="4952" class="Symbol">)</a> <a id="4954" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4956" class="Symbol">(</a><a id="4957" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a> <a id="4959" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4961" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4964" class="Symbol">)</a> <a id="5008" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="5012" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="5018" class="Symbol">(</a><a id="5019" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="5025" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="5027" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="5036" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="5046" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a><a id="5055" class="Symbol">)</a> <a id="5057" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="5059" href="Categories.Category.Core.html#1004" class="Function">sym-assoc</a> <a id="5069" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="5077" class="Symbol">(</a><a id="5078" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="5082" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5085" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="5089" class="Symbol">)</a> <a id="5091" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5093" class="Symbol">(</a><a id="5094" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="5096" class="Symbol">(</a><a id="5097" href="Monad.Instance.K.Commutative.html#3584" class="Bound">X</a> <a id="5099" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="5101" href="Monad.Instance.K.Commutative.html#3588" class="Bound">Y</a><a id="5102" class="Symbol">)</a> <a id="5104" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5107" href="Category.Ambient.html#2115" class="Function">idC</a><a id="5110" class="Symbol">)</a> <a id="5112" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5114" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="5128" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5130" class="Symbol">(</a><a id="5131" href="Monad.Instance.K.Commutative.html#3595" class="Bound">h</a> <a id="5133" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5135" href="Category.Ambient.html#2115" class="Function">idC</a><a id="5138" class="Symbol">)</a> <a id="5163" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
|
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<a id="σ-natural"></a><a id="5166" href="Monad.Instance.K.Commutative.html#5166" class="Function">σ-natural</a> <a id="5176" class="Symbol">:</a> <a id="5178" class="Symbol">∀</a> <a id="5180" class="Symbol">{</a><a id="5181" href="Monad.Instance.K.Commutative.html#5181" class="Bound">X</a> <a id="5183" href="Monad.Instance.K.Commutative.html#5183" class="Bound">Y</a> <a id="5185" href="Monad.Instance.K.Commutative.html#5185" class="Bound">Z</a> <a id="5187" href="Monad.Instance.K.Commutative.html#5187" class="Bound">U</a><a id="5188" class="Symbol">}</a> <a id="5190" class="Symbol">(</a><a id="5191" href="Monad.Instance.K.Commutative.html#5191" class="Bound">f</a> <a id="5193" class="Symbol">:</a> <a id="5195" href="Monad.Instance.K.Commutative.html#5181" class="Bound">X</a> <a id="5197" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="5199" href="Monad.Instance.K.Commutative.html#5183" class="Bound">Y</a><a id="5200" class="Symbol">)</a> <a id="5202" class="Symbol">(</a><a id="5203" href="Monad.Instance.K.Commutative.html#5203" class="Bound">g</a> <a id="5205" class="Symbol">:</a> <a id="5207" href="Monad.Instance.K.Commutative.html#5185" class="Bound">Z</a> <a id="5209" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="5211" href="Monad.Instance.K.Commutative.html#5187" class="Bound">U</a><a id="5212" class="Symbol">)</a> <a id="5214" class="Symbol">→</a> <a id="5216" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="5218" class="Symbol">_</a> <a id="5220" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5222" class="Symbol">(</a><a id="5223" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5227" href="Monad.Instance.K.Commutative.html#5191" class="Bound">f</a> <a id="5229" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5231" href="Monad.Instance.K.Commutative.html#5203" class="Bound">g</a><a id="5232" class="Symbol">)</a> <a id="5234" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="5236" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5240" class="Symbol">(</a><a id="5241" href="Monad.Instance.K.Commutative.html#5191" class="Bound">f</a> <a id="5243" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5245" href="Monad.Instance.K.Commutative.html#5203" class="Bound">g</a><a id="5246" class="Symbol">)</a> <a id="5248" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5250" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="5252" class="Symbol">_</a>
|
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<a id="5254" href="Monad.Instance.K.Commutative.html#5166" class="Function">σ-natural</a> <a id="5264" class="Symbol">{</a><a id="5265" href="Monad.Instance.K.Commutative.html#5265" class="Bound">X</a><a id="5266" class="Symbol">}</a> <a id="5268" class="Symbol">{</a><a id="5269" href="Monad.Instance.K.Commutative.html#5269" class="Bound">Y</a><a id="5270" class="Symbol">}</a> <a id="5272" class="Symbol">{</a><a id="5273" href="Monad.Instance.K.Commutative.html#5273" class="Bound">Z</a><a id="5274" class="Symbol">}</a> <a id="5276" class="Symbol">{</a><a id="5277" href="Monad.Instance.K.Commutative.html#5277" class="Bound">U</a><a id="5278" class="Symbol">}</a> <a id="5280" href="Monad.Instance.K.Commutative.html#5280" class="Bound">f</a> <a id="5282" href="Monad.Instance.K.Commutative.html#5282" class="Bound">g</a> <a id="5284" class="Symbol">=</a> <a id="5286" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
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<a id="5295" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="5297" class="Symbol">_</a> <a id="5299" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5301" class="Symbol">(</a><a id="5302" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5306" href="Monad.Instance.K.Commutative.html#5280" class="Bound">f</a> <a id="5308" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5310" href="Monad.Instance.K.Commutative.html#5282" class="Bound">g</a><a id="5311" class="Symbol">)</a> <a id="5335" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5338" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="5344" class="Symbol">(</a><a id="5345" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="5351" href="Categories.Category.BinaryProducts.html#4512" class="Function">swap∘⁂</a><a id="5357" class="Symbol">)</a> <a id="5359" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="5364" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5368" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="5373" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5375" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="5377" class="Symbol">_</a> <a id="5379" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5381" class="Symbol">(</a><a id="5382" href="Monad.Instance.K.Commutative.html#5282" class="Bound">g</a> <a id="5384" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5386" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5390" href="Monad.Instance.K.Commutative.html#5280" class="Bound">f</a><a id="5391" class="Symbol">)</a> <a id="5393" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5395" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="5404" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5407" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="5415" class="Symbol">((</a><a id="5417" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="5423" class="Symbol">(</a><a id="5424" href="Categories.NaturalTransformation.Core.html#827" class="Function">strengthen.commute</a> <a id="5443" class="Symbol">(</a><a id="5444" href="Monad.Instance.K.Commutative.html#5282" class="Bound">g</a> <a id="5446" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="5448" href="Monad.Instance.K.Commutative.html#5280" class="Bound">f</a><a id="5449" class="Symbol">)))</a> <a id="5453" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="5455" href="Categories.Category.Core.html#715" class="Function">assoc</a><a id="5460" class="Symbol">)</a> <a id="5462" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="5467" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5471" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="5476" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5478" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5482" class="Symbol">(</a><a id="5483" href="Monad.Instance.K.Commutative.html#5282" class="Bound">g</a> <a id="5485" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5487" href="Monad.Instance.K.Commutative.html#5280" class="Bound">f</a><a id="5488" class="Symbol">)</a> <a id="5490" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5492" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="5494" class="Symbol">_</a> <a id="5496" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5498" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="5507" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5510" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="5516" class="Symbol">(</a><a id="5517" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="5521" href="Categories.Functor.Core.html#565" class="Function">monadK.F.homomorphism</a><a id="5542" class="Symbol">)</a> <a id="5544" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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|
<a id="5549" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5553" class="Symbol">(</a><a id="5554" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="5559" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5561" class="Symbol">(</a><a id="5562" href="Monad.Instance.K.Commutative.html#5282" class="Bound">g</a> <a id="5564" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5566" href="Monad.Instance.K.Commutative.html#5280" class="Bound">f</a><a id="5567" class="Symbol">))</a> <a id="5570" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5572" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="5574" class="Symbol">_</a> <a id="5576" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5578" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="5589" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5592" class="Symbol">(</a><a id="5593" href="Categories.Functor.Core.html#696" class="Function">monadK.F.F-resp-≈</a> <a id="5611" href="Categories.Category.BinaryProducts.html#4512" class="Function">swap∘⁂</a><a id="5617" class="Symbol">)</a> <a id="5619" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="5627" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="5632" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5636" class="Symbol">((</a><a id="5638" href="Monad.Instance.K.Commutative.html#5280" class="Bound">f</a> <a id="5640" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5642" href="Monad.Instance.K.Commutative.html#5282" class="Bound">g</a><a id="5643" class="Symbol">)</a> <a id="5645" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5647" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="5651" class="Symbol">)</a> <a id="5653" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5655" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="5657" class="Symbol">_</a> <a id="5659" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5661" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="5672" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5675" href="Categories.Functor.Core.html#565" class="Function">monadK.F.homomorphism</a> <a id="5697" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="5705" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
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<a id="5710" class="Symbol">(</a><a id="5711" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5715" class="Symbol">((</a><a id="5717" href="Monad.Instance.K.Commutative.html#5280" class="Bound">f</a> <a id="5719" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5721" href="Monad.Instance.K.Commutative.html#5282" class="Bound">g</a><a id="5722" class="Symbol">))</a> <a id="5725" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5727" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5731" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="5735" class="Symbol">)</a> <a id="5737" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5739" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="5741" class="Symbol">_</a> <a id="5743" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5745" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="5750" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5753" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="5759" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="5764" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5768" class="Symbol">(</a><a id="5769" href="Monad.Instance.K.Commutative.html#5280" class="Bound">f</a> <a id="5771" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5773" href="Monad.Instance.K.Commutative.html#5282" class="Bound">g</a><a id="5774" class="Symbol">)</a> <a id="5776" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5778" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="5780" class="Symbol">_</a> <a id="5804" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
|
|||
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<a id="σ-μ-η-comm"></a><a id="5808" href="Monad.Instance.K.Commutative.html#5808" class="Function">σ-μ-η-comm</a> <a id="5819" class="Symbol">:</a> <a id="5821" class="Symbol">∀</a> <a id="5823" class="Symbol">{</a><a id="5824" href="Monad.Instance.K.Commutative.html#5824" class="Bound">A</a> <a id="5826" href="Monad.Instance.K.Commutative.html#5826" class="Bound">B</a><a id="5827" class="Symbol">}</a> <a id="5829" class="Symbol">→</a> <a id="5831" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="5835" class="Symbol">(</a><a id="5836" href="Monad.Instance.K.Commutative.html#5824" class="Bound">A</a> <a id="5838" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="5840" href="Monad.Instance.K.Commutative.html#5826" class="Bound">B</a><a id="5841" class="Symbol">)</a> <a id="5843" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5845" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5849" class="Symbol">(</a><a id="5850" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="5852" class="Symbol">_)</a> <a id="5855" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5857" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="5859" class="Symbol">_</a> <a id="5861" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="5863" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="5865" class="Symbol">_</a> <a id="5867" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5869" class="Symbol">(</a><a id="5870" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="5874" class="Symbol">_</a> <a id="5876" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5878" href="Category.Ambient.html#2115" class="Function">idC</a><a id="5881" class="Symbol">)</a>
|
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<a id="5883" href="Monad.Instance.K.Commutative.html#5808" class="Function">σ-μ-η-comm</a> <a id="5894" class="Symbol">{</a><a id="5895" href="Monad.Instance.K.Commutative.html#5895" class="Bound">A</a><a id="5896" class="Symbol">}</a> <a id="5898" class="Symbol">{</a><a id="5899" href="Monad.Instance.K.Commutative.html#5899" class="Bound">B</a><a id="5900" class="Symbol">}</a> <a id="5902" class="Symbol">=</a> <a id="5904" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
|||
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<a id="5913" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="5917" class="Symbol">(</a><a id="5918" href="Monad.Instance.K.Commutative.html#5895" class="Bound">A</a> <a id="5920" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="5922" href="Monad.Instance.K.Commutative.html#5899" class="Bound">B</a><a id="5923" class="Symbol">)</a> <a id="5925" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5927" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5931" class="Symbol">(</a><a id="5932" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="5934" class="Symbol">_)</a> <a id="5937" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5939" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="5941" class="Symbol">_</a> <a id="5963" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5966" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="5974" class="Symbol">(</a><a id="5975" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="5981" class="Symbol">(</a><a id="5982" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="5986" href="Categories.Functor.Core.html#565" class="Function">monadK.F.homomorphism</a><a id="6007" class="Symbol">))</a> <a id="6010" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="6015" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="6019" class="Symbol">_</a> <a id="6021" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6023" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6027" class="Symbol">(</a><a id="6028" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="6030" class="Symbol">_</a> <a id="6032" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6034" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="6038" class="Symbol">)</a> <a id="6040" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6042" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6044" class="Symbol">_</a> <a id="6046" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6048" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="6065" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6068" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="6076" class="Symbol">((</a><a id="6078" href="Categories.Functor.Core.html#696" class="Function">monadK.F.F-resp-≈</a> <a id="6096" class="Symbol">(</a><a id="6097" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="6103" class="Symbol">(</a><a id="6104" href="Categories.Morphism.Reasoning.Core.html#6665" class="Function">cancelʳ</a> <a id="6112" href="Categories.Category.BinaryProducts.html#4688" class="Function">swap∘swap</a><a id="6121" class="Symbol">)))</a> <a id="6125" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="6132" class="Symbol">)</a> <a id="6134" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="6139" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="6143" class="Symbol">_</a> <a id="6145" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6147" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6151" class="Symbol">(</a><a id="6152" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6156" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="6161" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6163" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6165" class="Symbol">_)</a> <a id="6168" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6170" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6172" class="Symbol">_</a> <a id="6174" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6176" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="6189" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6192" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="6200" class="Symbol">(</a><a id="6201" href="Categories.Functor.Core.html#565" class="Function">monadK.F.homomorphism</a> <a id="6223" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="6230" class="Symbol">)</a> <a id="6232" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="6237" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="6241" class="Symbol">_</a> <a id="6243" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6245" class="Symbol">(</a><a id="6246" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6250" class="Symbol">(</a><a id="6251" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6255" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="6259" class="Symbol">)</a> <a id="6261" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6263" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6267" class="Symbol">(</a><a id="6268" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6270" class="Symbol">_))</a> <a id="6274" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6276" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6278" class="Symbol">_</a> <a id="6280" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6282" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="6287" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6290" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="6296" class="Symbol">(</a><a id="6297" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="6303" class="Symbol">(</a><a id="6304" href="Categories.NaturalTransformation.Core.html#827" class="Function">μ.commute</a> <a id="6314" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="6318" class="Symbol">))</a> <a id="6321" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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|
<a id="6326" class="Symbol">(((</a><a id="6329" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6333" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="6337" class="Symbol">)</a> <a id="6339" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6341" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="6345" class="Symbol">_)</a> <a id="6348" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6350" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6354" class="Symbol">(</a><a id="6355" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6357" class="Symbol">_))</a> <a id="6361" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6363" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6365" class="Symbol">_</a> <a id="6367" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6369" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="6376" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6379" class="Symbol">(</a><a id="6380" href="Categories.Morphism.Reasoning.Core.html#1466" class="Function">assoc²</a> <a id="6387" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="6389" class="Symbol">(</a><a id="6390" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="6398" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="6402" href="Categories.Morphism.Reasoning.Core.html#1551" class="Function">assoc²'</a><a id="6409" class="Symbol">))</a> <a id="6412" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="6417" class="Symbol">(</a><a id="6418" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6422" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="6426" class="Symbol">)</a> <a id="6428" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6430" class="Symbol">(</a><a id="6431" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="6435" class="Symbol">_</a> <a id="6437" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6439" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6443" class="Symbol">(</a><a id="6444" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6446" class="Symbol">_)</a> <a id="6449" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6451" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6453" class="Symbol">_)</a> <a id="6456" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6458" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="6467" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6470" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="6478" class="Symbol">(</a><a id="6479" href="Categories.Morphism.Reasoning.Core.html#2485" class="Function">pushˡ</a> <a id="6485" href="Categories.Monad.Strong.html#1494" class="Function">strongK.μ-η-comm</a><a id="6501" class="Symbol">)</a> <a id="6503" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="6508" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6512" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="6517" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6519" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6521" class="Symbol">_</a> <a id="6523" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6525" class="Symbol">(</a><a id="6526" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="6530" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6532" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="6536" class="Symbol">_)</a> <a id="6539" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6541" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="6558" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="6562" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="6568" class="Symbol">(</a><a id="6569" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="6575" href="Categories.Category.BinaryProducts.html#4512" class="Function">swap∘⁂</a><a id="6581" class="Symbol">)</a> <a id="6583" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
|
|||
|
|
<a id="6588" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="6590" class="Symbol">_</a> <a id="6592" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6594" class="Symbol">(</a><a id="6595" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="6599" class="Symbol">_</a> <a id="6601" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6603" href="Category.Ambient.html#2115" class="Function">idC</a><a id="6606" class="Symbol">)</a> <a id="6638" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
|
|||
|
|
|
|||
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<a id="σ-π₁"></a><a id="6641" href="Monad.Instance.K.Commutative.html#6641" class="Function">σ-π₁</a> <a id="6646" class="Symbol">:</a> <a id="6648" class="Symbol">∀</a> <a id="6650" class="Symbol">{</a><a id="6651" href="Monad.Instance.K.Commutative.html#6651" class="Bound">A</a> <a id="6653" href="Monad.Instance.K.Commutative.html#6653" class="Bound">B</a><a id="6654" class="Symbol">}</a> <a id="6656" class="Symbol">→</a> <a id="6658" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6662" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="6665" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6667" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="6669" class="Symbol">(</a><a id="6670" href="Monad.Instance.K.Commutative.html#6651" class="Bound">A</a> <a id="6672" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="6674" href="Monad.Instance.K.Commutative.html#6653" class="Bound">B</a><a id="6675" class="Symbol">)</a> <a id="6677" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="6679" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a>
|
|||
|
|
<a id="6682" href="Monad.Instance.K.Commutative.html#6641" class="Function">σ-π₁</a> <a id="6687" class="Symbol">{</a><a id="6688" href="Monad.Instance.K.Commutative.html#6688" class="Bound">A</a><a id="6689" class="Symbol">}</a> <a id="6691" class="Symbol">{</a><a id="6692" href="Monad.Instance.K.Commutative.html#6692" class="Bound">B</a><a id="6693" class="Symbol">}</a> <a id="6695" class="Symbol">=</a> <a id="6697" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
|||
|
|
<a id="6706" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6710" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="6713" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6715" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="6717" class="Symbol">_</a> <a id="6726" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6729" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="6735" class="Symbol">(</a><a id="6736" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="6740" href="Categories.Functor.Core.html#565" class="Function">K.homomorphism</a> <a id="6755" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="6757" href="Categories.Functor.Core.html#696" class="Function">K.F-resp-≈</a> <a id="6768" href="Categories.Object.Product.Core.html#603" class="Function">project₁</a><a id="6776" class="Symbol">)</a> <a id="6778" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="6783" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="6787" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="6790" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6792" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="6794" class="Symbol">_</a> <a id="6796" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6798" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="6803" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6806" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="6812" class="Symbol">(</a><a id="6813" href="Monad.Instance.K.Strong.html#3453" class="Function">τ-π₂</a> <a id="6818" class="Symbol">(</a><a id="6819" href="Monad.Instance.K.Commutative.html#6692" class="Bound">B</a> <a id="6821" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="6823" href="Monad.Instance.K.Commutative.html#6688" class="Bound">A</a><a id="6824" class="Symbol">))</a> <a id="6827" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
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<a id="6832" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="6835" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6837" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="6852" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6855" href="Categories.Object.Product.Core.html#637" class="Function">project₂</a> <a id="6864" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="6869" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="6889" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
|
|||
|
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|
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<a id="σ-kleisli-assoc"></a><a id="6892" href="Monad.Instance.K.Commutative.html#6892" class="Function">σ-kleisli-assoc</a> <a id="6908" class="Symbol">:</a> <a id="6910" class="Symbol">∀</a> <a id="6912" class="Symbol">{</a><a id="6913" href="Monad.Instance.K.Commutative.html#6913" class="Bound">X</a> <a id="6915" href="Monad.Instance.K.Commutative.html#6915" class="Bound">Y</a> <a id="6917" href="Monad.Instance.K.Commutative.html#6917" class="Bound">Z</a> <a id="6919" href="Monad.Instance.K.Commutative.html#6919" class="Bound">U</a><a id="6920" class="Symbol">}</a> <a id="6922" class="Symbol">(</a><a id="6923" href="Monad.Instance.K.Commutative.html#6923" class="Bound">f</a> <a id="6925" class="Symbol">:</a> <a id="6927" href="Monad.Instance.K.Commutative.html#6913" class="Bound">X</a> <a id="6929" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="6931" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="6935" href="Monad.Instance.K.Commutative.html#6915" class="Bound">Y</a><a id="6936" class="Symbol">)</a> <a id="6938" class="Symbol">(</a><a id="6939" href="Monad.Instance.K.Commutative.html#6939" class="Bound">g</a> <a id="6941" class="Symbol">:</a> <a id="6943" href="Monad.Instance.K.Commutative.html#6917" class="Bound">Z</a> <a id="6945" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="6947" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="6951" href="Monad.Instance.K.Commutative.html#6919" class="Bound">U</a><a id="6952" class="Symbol">)</a> <a id="6954" class="Symbol">→</a> <a id="6956" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="6963" class="Symbol">(</a><a id="6964" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="6966" class="Symbol">_</a> <a id="6968" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6970" class="Symbol">(</a><a id="6971" href="Monad.Instance.K.Commutative.html#6923" class="Bound">f</a> <a id="6973" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6975" href="Category.Ambient.html#2115" class="Function">idC</a><a id="6978" class="Symbol">))</a> <a id="6981" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6983" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="6985" class="Symbol">_</a> <a id="6987" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="6989" class="Symbol">(</a><a id="6990" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="6994" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="6996" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7003" href="Monad.Instance.K.Commutative.html#6939" class="Bound">g</a><a id="7004" class="Symbol">)</a> <a id="7006" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="7008" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7010" class="Symbol">_</a> <a id="7012" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7014" class="Symbol">(</a><a id="7015" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7022" href="Monad.Instance.K.Commutative.html#6923" class="Bound">f</a> <a id="7024" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7026" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7033" href="Monad.Instance.K.Commutative.html#6939" class="Bound">g</a><a id="7034" class="Symbol">)</a>
|
|||
|
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<a id="7036" href="Monad.Instance.K.Commutative.html#6892" class="Function">σ-kleisli-assoc</a> <a id="7052" class="Symbol">{</a><a id="7053" href="Monad.Instance.K.Commutative.html#7053" class="Bound">X</a><a id="7054" class="Symbol">}</a> <a id="7056" class="Symbol">{</a><a id="7057" href="Monad.Instance.K.Commutative.html#7057" class="Bound">Y</a><a id="7058" class="Symbol">}</a> <a id="7060" class="Symbol">{</a><a id="7061" href="Monad.Instance.K.Commutative.html#7061" class="Bound">Z</a><a id="7062" class="Symbol">}</a> <a id="7064" class="Symbol">{</a><a id="7065" href="Monad.Instance.K.Commutative.html#7065" class="Bound">U</a><a id="7066" class="Symbol">}</a> <a id="7068" href="Monad.Instance.K.Commutative.html#7068" class="Bound">f</a> <a id="7070" href="Monad.Instance.K.Commutative.html#7070" class="Bound">g</a> <a id="7072" class="Symbol">=</a> <a id="7074" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
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<a id="7083" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7090" class="Symbol">(</a><a id="7091" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7093" class="Symbol">_</a> <a id="7095" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7097" class="Symbol">(</a><a id="7098" href="Monad.Instance.K.Commutative.html#7068" class="Bound">f</a> <a id="7100" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7102" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7105" class="Symbol">))</a> <a id="7108" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7110" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7112" class="Symbol">_</a> <a id="7114" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7116" class="Symbol">(</a><a id="7117" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="7121" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7123" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7130" href="Monad.Instance.K.Commutative.html#7070" class="Bound">g</a><a id="7131" class="Symbol">)</a> <a id="7138" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="7142" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="7148" class="Symbol">(</a><a id="7149" href="Category.Ambient.html#10469" class="Function">extend∘F₁</a> <a id="7159" href="Monad.Instance.K.html#1609" class="Function">monadK</a> <a id="7166" class="Symbol">(</a><a id="7167" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7169" class="Symbol">_)</a> <a id="7172" class="Symbol">(</a><a id="7173" href="Monad.Instance.K.Commutative.html#7068" class="Bound">f</a> <a id="7175" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7177" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7180" class="Symbol">))</a> <a id="7183" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="7188" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7195" class="Symbol">(</a><a id="7196" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7198" class="Symbol">_)</a> <a id="7201" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7203" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="7207" class="Symbol">(</a><a id="7208" href="Monad.Instance.K.Commutative.html#7068" class="Bound">f</a> <a id="7210" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7212" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7215" class="Symbol">)</a> <a id="7217" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7219" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7221" class="Symbol">_</a> <a id="7223" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7225" class="Symbol">(</a><a id="7226" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="7230" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7232" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7239" href="Monad.Instance.K.Commutative.html#7070" class="Bound">g</a><a id="7240" class="Symbol">)</a> <a id="7243" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="7246" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="7254" class="Symbol">(</a><a id="7255" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="7261" class="Symbol">(</a><a id="7262" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="7266" class="Symbol">(</a><a id="7267" href="Monad.Instance.K.Commutative.html#5166" class="Function">σ-natural</a> <a id="7277" href="Monad.Instance.K.Commutative.html#7068" class="Bound">f</a> <a id="7279" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7282" class="Symbol">))</a> <a id="7285" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="7287" href="Categories.Category.Core.html#715" class="Function">assoc</a><a id="7292" class="Symbol">)</a> <a id="7294" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="7299" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7306" class="Symbol">(</a><a id="7307" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7309" class="Symbol">_)</a> <a id="7312" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7314" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7316" class="Symbol">_</a> <a id="7318" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7320" class="Symbol">(</a><a id="7321" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="7325" href="Monad.Instance.K.Commutative.html#7068" class="Bound">f</a> <a id="7327" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7329" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7332" class="Symbol">)</a> <a id="7334" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7336" class="Symbol">(</a><a id="7337" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="7341" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7343" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7350" href="Monad.Instance.K.Commutative.html#7070" class="Bound">g</a><a id="7351" class="Symbol">)</a> <a id="7354" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="7357" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="7363" class="Symbol">(</a><a id="7364" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="7370" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="7372" href="Monad.Instance.K.Commutative.html#5808" class="Function">σ-μ-η-comm</a><a id="7382" class="Symbol">)</a> <a id="7384" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="7386" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="7392" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="7396" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7398" class="Symbol">_</a> <a id="7400" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7402" class="Symbol">(</a><a id="7403" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="7407" class="Symbol">_</a> <a id="7409" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7411" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7414" class="Symbol">)</a> <a id="7416" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7418" class="Symbol">(</a><a id="7419" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="7423" href="Monad.Instance.K.Commutative.html#7068" class="Bound">f</a> <a id="7425" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7427" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7430" class="Symbol">)</a> <a id="7432" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7434" class="Symbol">(</a><a id="7435" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="7439" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7441" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7448" href="Monad.Instance.K.Commutative.html#7070" class="Bound">g</a><a id="7449" class="Symbol">)</a> <a id="7451" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="7454" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="7462" class="Symbol">(</a><a id="7463" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="7469" class="Symbol">(</a><a id="7470" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="7474" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="7476" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="7484" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="7489" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="7498" class="Symbol">))</a> <a id="7501" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="7506" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7508" class="Symbol">_</a> <a id="7510" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7512" class="Symbol">(</a><a id="7513" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7520" href="Monad.Instance.K.Commutative.html#7068" class="Bound">f</a> <a id="7522" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7524" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7527" class="Symbol">)</a> <a id="7529" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7531" class="Symbol">(</a><a id="7532" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="7536" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7538" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7545" href="Monad.Instance.K.Commutative.html#7070" class="Bound">g</a><a id="7546" class="Symbol">)</a> <a id="7561" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="7564" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="7572" class="Symbol">(</a><a id="7573" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="7577" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="7579" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="7587" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a> <a id="7597" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="7606" class="Symbol">)</a> <a id="7608" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
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<a id="7612" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="7614" class="Symbol">_</a> <a id="7616" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7618" class="Symbol">(</a><a id="7619" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7626" href="Monad.Instance.K.Commutative.html#7068" class="Bound">f</a> <a id="7628" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7630" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7637" href="Monad.Instance.K.Commutative.html#7070" class="Bound">g</a><a id="7638" class="Symbol">)</a> <a id="7640" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="τ-kleisli-assoc"></a><a id="7643" href="Monad.Instance.K.Commutative.html#7643" class="Function">τ-kleisli-assoc</a> <a id="7659" class="Symbol">:</a> <a id="7661" class="Symbol">∀</a> <a id="7663" class="Symbol">{</a><a id="7664" href="Monad.Instance.K.Commutative.html#7664" class="Bound">X</a> <a id="7666" href="Monad.Instance.K.Commutative.html#7666" class="Bound">Y</a> <a id="7668" href="Monad.Instance.K.Commutative.html#7668" class="Bound">Z</a> <a id="7670" href="Monad.Instance.K.Commutative.html#7670" class="Bound">U</a><a id="7671" class="Symbol">}</a> <a id="7673" class="Symbol">(</a><a id="7674" href="Monad.Instance.K.Commutative.html#7674" class="Bound">f</a> <a id="7676" class="Symbol">:</a> <a id="7678" href="Monad.Instance.K.Commutative.html#7664" class="Bound">X</a> <a id="7680" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="7682" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="7686" href="Monad.Instance.K.Commutative.html#7666" class="Bound">Y</a><a id="7687" class="Symbol">)</a> <a id="7689" class="Symbol">(</a><a id="7690" href="Monad.Instance.K.Commutative.html#7690" class="Bound">g</a> <a id="7692" class="Symbol">:</a> <a id="7694" href="Monad.Instance.K.Commutative.html#7668" class="Bound">Z</a> <a id="7696" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="7698" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="7702" href="Monad.Instance.K.Commutative.html#7670" class="Bound">U</a><a id="7703" class="Symbol">)</a> <a id="7705" class="Symbol">→</a> <a id="7707" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7714" class="Symbol">(</a><a id="7715" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="7717" class="Symbol">_</a> <a id="7719" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7721" class="Symbol">(</a><a id="7722" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="7726" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7728" href="Monad.Instance.K.Commutative.html#7690" class="Bound">g</a><a id="7729" class="Symbol">))</a> <a id="7732" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7734" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="7736" class="Symbol">_</a> <a id="7738" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7740" class="Symbol">(</a><a id="7741" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7748" href="Monad.Instance.K.Commutative.html#7674" class="Bound">f</a> <a id="7750" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7752" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7755" class="Symbol">)</a> <a id="7757" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="7759" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="7761" class="Symbol">_</a> <a id="7763" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7765" class="Symbol">(</a><a id="7766" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7773" href="Monad.Instance.K.Commutative.html#7674" class="Bound">f</a> <a id="7775" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7777" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7784" href="Monad.Instance.K.Commutative.html#7690" class="Bound">g</a><a id="7785" class="Symbol">)</a>
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<a id="7787" href="Monad.Instance.K.Commutative.html#7643" class="Function">τ-kleisli-assoc</a> <a id="7803" class="Symbol">{</a><a id="7804" href="Monad.Instance.K.Commutative.html#7804" class="Bound">X</a><a id="7805" class="Symbol">}</a> <a id="7807" class="Symbol">{</a><a id="7808" href="Monad.Instance.K.Commutative.html#7808" class="Bound">Y</a><a id="7809" class="Symbol">}</a> <a id="7811" class="Symbol">{</a><a id="7812" href="Monad.Instance.K.Commutative.html#7812" class="Bound">Z</a><a id="7813" class="Symbol">}</a> <a id="7815" class="Symbol">{</a><a id="7816" href="Monad.Instance.K.Commutative.html#7816" class="Bound">U</a><a id="7817" class="Symbol">}</a> <a id="7819" href="Monad.Instance.K.Commutative.html#7819" class="Bound">f</a> <a id="7821" href="Monad.Instance.K.Commutative.html#7821" class="Bound">g</a> <a id="7823" class="Symbol">=</a> <a id="7825" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
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<a id="7834" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7841" class="Symbol">(</a><a id="7842" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="7844" class="Symbol">_</a> <a id="7846" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7848" class="Symbol">(</a><a id="7849" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="7853" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7855" href="Monad.Instance.K.Commutative.html#7821" class="Bound">g</a><a id="7856" class="Symbol">))</a> <a id="7859" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7861" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="7863" class="Symbol">_</a> <a id="7865" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7867" class="Symbol">(</a><a id="7868" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7875" href="Monad.Instance.K.Commutative.html#7819" class="Bound">f</a> <a id="7877" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7879" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7882" class="Symbol">)</a> <a id="7891" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="7895" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="7901" class="Symbol">(</a><a id="7902" href="Category.Ambient.html#10469" class="Function">extend∘F₁</a> <a id="7912" href="Monad.Instance.K.html#1609" class="Function">monadK</a> <a id="7919" class="Symbol">(</a><a id="7920" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="7922" class="Symbol">_)</a> <a id="7925" class="Symbol">(</a><a id="7926" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="7930" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7932" href="Monad.Instance.K.Commutative.html#7821" class="Bound">g</a><a id="7933" class="Symbol">))</a> <a id="7936" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="7941" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7948" class="Symbol">(</a><a id="7949" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="7951" class="Symbol">_)</a> <a id="7954" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7956" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="7960" class="Symbol">(</a><a id="7961" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="7965" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7967" href="Monad.Instance.K.Commutative.html#7821" class="Bound">g</a><a id="7968" class="Symbol">)</a> <a id="7970" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7972" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="7974" class="Symbol">_</a> <a id="7976" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="7978" class="Symbol">(</a><a id="7979" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="7986" href="Monad.Instance.K.Commutative.html#7819" class="Bound">f</a> <a id="7988" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="7990" href="Category.Ambient.html#2115" class="Function">idC</a><a id="7993" class="Symbol">)</a> <a id="7998" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="8001" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="8009" class="Symbol">(</a><a id="8010" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="8016" class="Symbol">(</a><a id="8017" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="8021" class="Symbol">(</a><a id="8022" href="Categories.NaturalTransformation.Core.html#827" class="Function">strengthen.commute</a> <a id="8041" class="Symbol">(</a><a id="8042" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="8046" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="8048" href="Monad.Instance.K.Commutative.html#7821" class="Bound">g</a><a id="8049" class="Symbol">)))</a> <a id="8053" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="8055" href="Categories.Category.Core.html#715" class="Function">assoc</a><a id="8060" class="Symbol">)</a> <a id="8062" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="8067" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="8074" class="Symbol">(</a><a id="8075" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="8077" class="Symbol">_)</a> <a id="8080" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8082" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="8084" class="Symbol">_</a> <a id="8086" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8088" class="Symbol">(</a><a id="8089" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="8093" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="8095" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="8099" href="Monad.Instance.K.Commutative.html#7821" class="Bound">g</a><a id="8100" class="Symbol">)</a> <a id="8102" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8104" class="Symbol">(</a><a id="8105" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="8112" href="Monad.Instance.K.Commutative.html#7819" class="Bound">f</a> <a id="8114" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="8116" href="Category.Ambient.html#2115" class="Function">idC</a><a id="8119" class="Symbol">)</a> <a id="8124" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="8127" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="8133" class="Symbol">(</a><a id="8134" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="8140" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="8142" href="Categories.Monad.Strong.html#1494" class="Function">strongK.μ-η-comm</a><a id="8158" class="Symbol">)</a> <a id="8160" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="8165" class="Symbol">(</a><a id="8166" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="8168" class="Symbol">_</a> <a id="8170" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8172" class="Symbol">(</a><a id="8173" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="8177" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="8179" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="8183" class="Symbol">_))</a> <a id="8187" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8189" class="Symbol">(</a><a id="8190" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="8194" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="8196" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="8200" href="Monad.Instance.K.Commutative.html#7821" class="Bound">g</a><a id="8201" class="Symbol">)</a> <a id="8203" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8205" class="Symbol">(</a><a id="8206" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="8213" href="Monad.Instance.K.Commutative.html#7819" class="Bound">f</a> <a id="8215" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="8217" href="Category.Ambient.html#2115" class="Function">idC</a><a id="8220" class="Symbol">)</a> <a id="8222" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="8225" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="8231" class="Symbol">(</a><a id="8232" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="8238" class="Symbol">(</a><a id="8239" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="8243" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="8245" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="8253" href="Categories.Category.Core.html#1339" class="Function">identity²</a> <a id="8263" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="8267" class="Symbol">))</a> <a id="8270" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="8274" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="8276" class="Symbol">_</a> <a id="8278" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8280" class="Symbol">(</a><a id="8281" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="8285" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="8287" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="8294" href="Monad.Instance.K.Commutative.html#7821" class="Bound">g</a><a id="8295" class="Symbol">)</a> <a id="8297" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8299" class="Symbol">(</a><a id="8300" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="8307" href="Monad.Instance.K.Commutative.html#7819" class="Bound">f</a> <a id="8309" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="8311" href="Category.Ambient.html#2115" class="Function">idC</a><a id="8314" class="Symbol">)</a> <a id="8331" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="8334" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="8342" class="Symbol">(</a><a id="8343" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="8347" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="8349" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="8357" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="8367" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a><a id="8376" class="Symbol">)</a> <a id="8378" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="8383" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="8385" class="Symbol">_</a> <a id="8387" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8389" class="Symbol">(</a><a id="8390" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="8397" href="Monad.Instance.K.Commutative.html#7819" class="Bound">f</a> <a id="8399" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="8401" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="8408" href="Monad.Instance.K.Commutative.html#7821" class="Bound">g</a><a id="8409" class="Symbol">)</a> <a id="8440" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="8444" class="Comment">-- TODO move to ambient</a>
|
|||
|
|
<a id="[⟨⟩]≈⟨[]⟩"></a><a id="8468" href="Monad.Instance.K.Commutative.html#8468" class="Function">[⟨⟩]≈⟨[]⟩</a> <a id="8478" class="Symbol">:</a> <a id="8480" class="Symbol">∀</a> <a id="8482" class="Symbol">{</a><a id="8483" href="Monad.Instance.K.Commutative.html#8483" class="Bound">A</a> <a id="8485" href="Monad.Instance.K.Commutative.html#8485" class="Bound">B</a> <a id="8487" href="Monad.Instance.K.Commutative.html#8487" class="Bound">C</a> <a id="8489" href="Monad.Instance.K.Commutative.html#8489" class="Bound">D</a><a id="8490" class="Symbol">}</a> <a id="8492" class="Symbol">(</a><a id="8493" href="Monad.Instance.K.Commutative.html#8493" class="Bound">f</a> <a id="8495" class="Symbol">:</a> <a id="8497" href="Monad.Instance.K.Commutative.html#8483" class="Bound">A</a> <a id="8499" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="8501" href="Monad.Instance.K.Commutative.html#8485" class="Bound">B</a><a id="8502" class="Symbol">)</a> <a id="8504" class="Symbol">(</a><a id="8505" href="Monad.Instance.K.Commutative.html#8505" class="Bound">g</a> <a id="8507" class="Symbol">:</a> <a id="8509" href="Monad.Instance.K.Commutative.html#8483" class="Bound">A</a> <a id="8511" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="8513" href="Monad.Instance.K.Commutative.html#8487" class="Bound">C</a><a id="8514" class="Symbol">)</a> <a id="8516" class="Symbol">(</a><a id="8517" href="Monad.Instance.K.Commutative.html#8517" class="Bound">h</a> <a id="8519" class="Symbol">:</a> <a id="8521" href="Monad.Instance.K.Commutative.html#8489" class="Bound">D</a> <a id="8523" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="8525" href="Monad.Instance.K.Commutative.html#8485" class="Bound">B</a><a id="8526" class="Symbol">)</a> <a id="8528" class="Symbol">(</a><a id="8529" href="Monad.Instance.K.Commutative.html#8529" class="Bound">i</a> <a id="8531" class="Symbol">:</a> <a id="8533" href="Monad.Instance.K.Commutative.html#8489" class="Bound">D</a> <a id="8535" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="8537" href="Monad.Instance.K.Commutative.html#8487" class="Bound">C</a><a id="8538" class="Symbol">)</a> <a id="8540" class="Symbol">→</a> <a id="8542" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="8544" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="8546" href="Monad.Instance.K.Commutative.html#8493" class="Bound">f</a> <a id="8548" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="8550" href="Monad.Instance.K.Commutative.html#8505" class="Bound">g</a> <a id="8552" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="8554" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="8556" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="8558" href="Monad.Instance.K.Commutative.html#8517" class="Bound">h</a> <a id="8560" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="8562" href="Monad.Instance.K.Commutative.html#8529" class="Bound">i</a> <a id="8564" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="8566" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="8568" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="8570" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="8572" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="8574" href="Monad.Instance.K.Commutative.html#8493" class="Bound">f</a> <a id="8576" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="8578" href="Monad.Instance.K.Commutative.html#8517" class="Bound">h</a> <a id="8580" href="Categories.Object.Coproduct.html#532" class="Function Operat
|
|||
|
|
<a id="8596" href="Monad.Instance.K.Commutative.html#8468" class="Function">[⟨⟩]≈⟨[]⟩</a> <a id="8606" href="Monad.Instance.K.Commutative.html#8606" class="Bound">f</a> <a id="8608" href="Monad.Instance.K.Commutative.html#8608" class="Bound">g</a> <a id="8610" href="Monad.Instance.K.Commutative.html#8610" class="Bound">h</a> <a id="8612" href="Monad.Instance.K.Commutative.html#8612" class="Bound">i</a> <a id="8614" class="Symbol">=</a> <a id="8616" href="Category.Ambient.html#2218" class="Function">[]-unique</a> <a id="8626" class="Symbol">(</a><a id="8627" href="Categories.Category.BinaryProducts.html#2975" class="Function">⟨⟩∘</a> <a id="8631" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="8633" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="8642" href="Categories.Object.Coproduct.html#569" class="Function">inject₁</a> <a id="8650" href="Categories.Object.Coproduct.html#569" class="Function">inject₁</a><a id="8657" class="Symbol">)</a> <a id="8659" class="Symbol">(</a><a id="8660" href="Categories.Category.BinaryProducts.html#2975" class="Function">⟨⟩∘</a> <a id="8664" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="8666" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="8675" href="Categories.Object.Coproduct.html#602" class="Function">inject₂</a> <a id="8683" href="Categories.Object.Coproduct.html#602" class="Function">inject₂</a><a id="8690" class="Symbol">)</a>
|
|||
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|
|
|||
|
|
<a id="8693" class="Comment">-- TODO move to K</a>
|
|||
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|
<a id="extend-preserve"></a><a id="8711" href="Monad.Instance.K.Commutative.html#8711" class="Function">extend-preserve</a> <a id="8727" class="Symbol">:</a> <a id="8729" class="Symbol">∀</a> <a id="8731" class="Symbol">{</a><a id="8732" href="Monad.Instance.K.Commutative.html#8732" class="Bound">X</a> <a id="8734" href="Monad.Instance.K.Commutative.html#8734" class="Bound">Y</a> <a id="8736" href="Monad.Instance.K.Commutative.html#8736" class="Bound">Z</a><a id="8737" class="Symbol">}</a> <a id="8739" class="Symbol">(</a><a id="8740" href="Monad.Instance.K.Commutative.html#8740" class="Bound">f</a> <a id="8742" class="Symbol">:</a> <a id="8744" href="Monad.Instance.K.Commutative.html#8732" class="Bound">X</a> <a id="8746" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="8748" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="8752" href="Monad.Instance.K.Commutative.html#8734" class="Bound">Y</a><a id="8753" class="Symbol">)</a> <a id="8755" class="Symbol">(</a><a id="8756" href="Monad.Instance.K.Commutative.html#8756" class="Bound">h</a> <a id="8758" class="Symbol">:</a> <a id="8760" href="Monad.Instance.K.Commutative.html#8736" class="Bound">Z</a> <a id="8762" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="8764" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="8768" href="Monad.Instance.K.Commutative.html#8732" class="Bound">X</a> <a id="8770" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="8772" href="Monad.Instance.K.Commutative.html#8736" class="Bound">Z</a><a id="8773" class="Symbol">)</a> <a id="8775" class="Symbol">→</a> <a id="8777" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="8784" href="Monad.Instance.K.Commutative.html#8740" class="Bound">f</a> <a id="8786" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8788" href="Monad.Instance.K.Commutative.html#8756" class="Bound">h</a> <a id="8790" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="8792" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="8794" class="Symbol">((</a><a id="8796" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="8803" href="Monad.Instance.K.Commutative.html#8740" class="Bound">f</a> <a id="8805" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="8808" href="Category.Ambient.html#2115" class="Function">idC</a><a id="8811" class="Symbol">)</a> <a id="8813" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8815" href="Monad.Instance.K.Commutative.html#8756" class="Bound">h</a><a id="8816" class="Symbol">)</a> <a id="8818" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
|
|||
|
|
<a id="8820" href="Monad.Instance.K.Commutative.html#8711" class="Function">extend-preserve</a> <a id="8836" class="Symbol">{</a><a id="8837" href="Monad.Instance.K.Commutative.html#8837" class="Bound">X</a><a id="8838" class="Symbol">}</a> <a id="8840" class="Symbol">{</a><a id="8841" href="Monad.Instance.K.Commutative.html#8841" class="Bound">Y</a><a id="8842" class="Symbol">}</a> <a id="8844" class="Symbol">{</a><a id="8845" href="Monad.Instance.K.Commutative.html#8845" class="Bound">Z</a><a id="8846" class="Symbol">}</a> <a id="8848" href="Monad.Instance.K.Commutative.html#8848" class="Bound">f</a> <a id="8850" href="Monad.Instance.K.Commutative.html#8850" class="Bound">h</a> <a id="8852" class="Symbol">=</a> <a id="8854" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
|||
|
|
<a id="8862" class="Symbol">(</a><a id="8863" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="8867" class="Symbol">_</a> <a id="8869" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8871" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="8875" href="Monad.Instance.K.Commutative.html#8848" class="Bound">f</a><a id="8876" class="Symbol">)</a> <a id="8878" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8880" href="Monad.Instance.K.Commutative.html#8850" class="Bound">h</a> <a id="8882" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="8902" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="8905" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="8911" class="Symbol">(</a><a id="8912" href="Category.Construction.ElgotAlgebras.html#812" class="Field">Elgot-Algebra-Morphism.preserves</a> <a id="8945" class="Symbol">(((</a><a id="8948" href="Monad.Instance.K.html#1182" class="Field">freealgebras</a> <a id="8961" class="Symbol">_)</a> <a id="8964" href="Categories.FreeObjects.Free.html#880" class="Field Operator">FreeObject.*</a><a id="8976" class="Symbol">)</a> <a id="8978" class="Symbol">(</a><a id="8979" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="8981" class="Symbol">_</a> <a id="8983" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8985" href="Monad.Instance.K.Commutative.html#8848" class="Bound">f</a><a id="8986" class="Symbol">)))</a> <a id="8990" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="9112" class="Symbol">((</a><a id="9114" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="9118" class="Symbol">_</a> <a id="9120" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9123" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9126" class="Symbol">)</a> <a id="9128" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9130" class="Symbol">(</a><a id="9131" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="9135" href="Monad.Instance.K.Commutative.html#8848" class="Bound">f</a> <a id="9137" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9140" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9143" class="Symbol">)</a> <a id="9145" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9147" href="Monad.Instance.K.Commutative.html#8850" class="Bound">h</a><a id="9148" class="Symbol">)</a> <a id="9150" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="9152" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="9155" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="9164" class="Symbol">(</a><a id="9165" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="9174" class="Symbol">_)</a> <a id="9177" class="Symbol">(</a><a id="9178" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="9184" class="Symbol">(</a><a id="9185" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="9191" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="9193" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="9202" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="9207" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="9216" class="Symbol">))</a> <a id="9219" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="9223" class="Symbol">((</a><a id="9225" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="9232" href="Monad.Instance.K.Commutative.html#8848" class="Bound">f</a> <a id="9234" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9237" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9240" class="Symbol">)</a> <a id="9242" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9244" href="Monad.Instance.K.Commutative.html#8850" class="Bound">h</a><a id="9245" class="Symbol">)</a> <a id="9247" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="9263" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
|
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<a id="9266" class="Keyword">private</a>
|
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<a id="comm-helper"></a><a id="9276" href="Monad.Instance.K.Commutative.html#9276" class="Function">comm-helper</a> <a id="9288" class="Symbol">:</a> <a id="9290" class="Symbol">∀</a> <a id="9292" class="Symbol">{</a><a id="9293" href="Monad.Instance.K.Commutative.html#9293" class="Bound">X</a> <a id="9295" href="Monad.Instance.K.Commutative.html#9295" class="Bound">Y</a> <a id="9297" href="Monad.Instance.K.Commutative.html#9297" class="Bound">Z</a> <a id="9299" href="Monad.Instance.K.Commutative.html#9299" class="Bound">U</a><a id="9300" class="Symbol">}</a> <a id="9302" class="Symbol">(</a><a id="9303" href="Monad.Instance.K.Commutative.html#9303" class="Bound">f</a> <a id="9305" class="Symbol">:</a> <a id="9307" href="Monad.Instance.K.Commutative.html#9293" class="Bound">X</a> <a id="9309" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="9311" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="9315" href="Monad.Instance.K.Commutative.html#9295" class="Bound">Y</a> <a id="9317" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="9319" href="Monad.Instance.K.Commutative.html#9293" class="Bound">X</a><a id="9320" class="Symbol">)</a> <a id="9322" class="Symbol">(</a><a id="9323" href="Monad.Instance.K.Commutative.html#9323" class="Bound">g</a> <a id="9325" class="Symbol">:</a> <a id="9327" href="Monad.Instance.K.Commutative.html#9297" class="Bound">Z</a> <a id="9329" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="9331" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="9335" href="Monad.Instance.K.Commutative.html#9299" class="Bound">U</a> <a id="9337" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="9339" href="Monad.Instance.K.Commutative.html#9297" class="Bound">Z</a><a id="9340" class="Symbol">)</a> <a id="9342" class="Symbol">→</a> <a id="9344" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="9351" class="Symbol">(</a><a id="9352" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="9354" class="Symbol">_)</a> <a id="9357" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9359" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="9361" class="Symbol">_</a> <a id="9363" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9365" class="Symbol">(((</a><a id="9368" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="9370" class="Symbol">_</a> <a id="9372" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9375" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9378" class="Symbol">)</a> <a id="9380" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9382" href="Monad.Instance.K.Commutative.html#9303" class="Bound">f</a><a id="9383" class="Symbol">)</a> <a id="9385" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="9387" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="9389" class="Symbol">((</a><a id="9391" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="9393" class="Symbol">_</a> <a id="9395" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9398" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9401" class="Symbol">)</a> <a id="9403" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9405" href="Monad.Instance.K.Commutative.html#9323" class="Bound">g</a><a id="9406" class="Symbol">)</a> <a id="9408" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="9409" class="Symbol">)</a> <a id="9411" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="9413" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="9420" class=
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<a id="9482" href="Monad.Instance.K.Commutative.html#9276" class="Function">comm-helper</a> <a id="9494" class="Symbol">{</a><a id="9495" href="Monad.Instance.K.Commutative.html#9495" class="Bound">X</a><a id="9496" class="Symbol">}</a> <a id="9498" class="Symbol">{</a><a id="9499" href="Monad.Instance.K.Commutative.html#9499" class="Bound">Y</a><a id="9500" class="Symbol">}</a> <a id="9502" class="Symbol">{</a><a id="9503" href="Monad.Instance.K.Commutative.html#9503" class="Bound">Z</a><a id="9504" class="Symbol">}</a> <a id="9506" class="Symbol">{</a><a id="9507" href="Monad.Instance.K.Commutative.html#9507" class="Bound">U</a><a id="9508" class="Symbol">}</a> <a id="9510" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="9512" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a> <a id="9514" class="Symbol">=</a> <a id="9516" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="9527" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="9534" class="Symbol">(</a><a id="9535" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="9537" class="Symbol">_)</a> <a id="9540" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9542" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="9544" class="Symbol">_</a> <a id="9546" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9548" class="Symbol">(</a><a id="9549" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="9552" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="9554" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="9556" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="9559" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="9560" class="Symbol">)</a> <a id="9594" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="9597" href="Monad.Instance.K.Commutative.html#29549" class="Function">τσ</a> <a id="9600" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="9607" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="9614" class="Symbol">(</a><a id="9615" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="9617" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="9619" class="Symbol">_</a> <a id="9621" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9623" class="Symbol">(</a> <a id="9625" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="9628" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="9630" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="9632" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="9636" class="Symbol">)</a> <a id="9638" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="9640" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="9642" class="Symbol">_</a> <a id="9644" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9646" class="Symbol">(</a><a id="9647" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="9651" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="9653" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="9656" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="9657" class="Symbol">)</a> <a id="9659" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="9660" class="Symbol">)</a> <a id="9662" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9664" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="9666" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="9674" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="9677" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="9681" href="Monad.Instance.K.Commutative.html#34683" class="Function">στ</a> <a id="9684" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="9691" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="9698" class="Symbol">(</a><a id="9699" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="9701" class="Symbol">_)</a> <a id="9704" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9706" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="9708" class="Symbol">_</a> <a id="9710" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9712" class="Symbol">(((</a><a id="9715" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="9717" class="Symbol">_</a> <a id="9719" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9722" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9725" class="Symbol">)</a> <a id="9727" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9729" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a><a id="9730" class="Symbol">)</a> <a id="9732" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="9734" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="9736" class="Symbol">((</a><a id="9738" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="9740" class="Symbol">_</a> <a id="9742" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9745" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9748" class="Symbol">)</a> <a id="9750" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9752" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="9753" class="Symbol">)</a> <a id="9755" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="9756" class="Symbol">)</a> <a id="9758" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="9764" class="Keyword">where</a>
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<a id="9776" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="9779" class="Symbol">=</a> <a id="9781" class="Symbol">(</a><a id="9782" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="9784" class="Symbol">_</a> <a id="9786" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9789" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9792" class="Symbol">)</a> <a id="9794" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9796" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a>
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<a id="9804" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="9807" class="Symbol">=</a> <a id="9809" class="Symbol">(</a><a id="9810" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="9812" class="Symbol">_</a> <a id="9814" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9817" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9820" class="Symbol">)</a> <a id="9822" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9824" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a>
|
|||
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<a id="9832" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="9834" class="Symbol">=</a> <a id="9836" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="9838" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="9841" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9843" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="9847" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="9850" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9852" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="9854" class="Symbol">_</a> <a id="9856" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="9858" class="Symbol">(</a><a id="9859" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="9863" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a> <a id="9866" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9868" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="9870" class="Symbol">_</a> <a id="9872" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9875" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9878" class="Symbol">)</a> <a id="9880" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9882" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="9896" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9898" class="Symbol">(</a><a id="9899" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="9902" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="9904" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9907" class="Symbol">)</a> <a id="9909" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="9911" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9913" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="9927" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9929" class="Symbol">(</a><a id="9930" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="9934" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="9936" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="9938" class="Symbol">)</a>
|
|||
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<a id="9946" href="Monad.Instance.K.Commutative.html#9946" class="Function">w-law₁</a> <a id="9953" class="Symbol">:</a> <a id="9955" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="9958" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="9960" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9962" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="9965" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="9967" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="9974" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="9976" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="9979" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="9981" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9983" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="9986" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="9988" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="9990" class="Symbol">_</a> <a id="9992" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9994" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="9997" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="9999" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10001" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="10003" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
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<a id="10011" href="Monad.Instance.K.Commutative.html#9946" class="Function">w-law₁</a> <a id="10018" class="Symbol">=</a> <a id="10020" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="10024" class="Symbol">(</a><a id="10025" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="10039" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="10046" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="10048" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="10051" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="10053" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10055" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10058" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="10060" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="10062" class="Symbol">_</a> <a id="10064" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10066" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10069" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="10071" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10073" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="10075" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="10171" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="10174" href="Monad.Instance.K.Commutative.html#11937" class="Function">step₁</a> <a id="10180" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="10190" class="Symbol">(</a><a id="10191" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="10193" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="10196" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10198" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10201" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="10203" class="Symbol">(</a><a id="10204" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="10207" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="10209" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10211" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10214" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="10217" href="Category.Ambient.html#2115" class="Function">idC</a><a id="10220" class="Symbol">)</a> <a id="10222" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10224" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="10238" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="10240" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10242" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="10256" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10258" class="Symbol">(</a><a id="10259" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="10262" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="10264" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="10265" class="Symbol">))</a><a id="10267" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="10322" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="10325" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="10329" href="Monad.Instance.K.Commutative.html#18601" class="Function">step₂</a> <a id="10335" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="10345" class="Symbol">(</a><a id="10346" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="10349" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="10350" class="Symbol">)</a> <a id="10352" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10354" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10477" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a><a id="10478" class="Symbol">)</a>
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<a id="10488" class="Keyword">where</a>
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<a id="10504" href="Monad.Instance.K.Commutative.html#10504" class="Function">h</a> <a id="10506" class="Symbol">=</a> <a id="10508" class="Symbol">(</a><a id="10509" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10512" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="10515" class="Symbol">(</a><a id="10516" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10519" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="10522" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10525" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="10527" href="Category.Ambient.html#2115" class="Function">idC</a><a id="10530" class="Symbol">)</a> <a id="10532" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10534" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="10548" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10550" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="10552" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="10556" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="10558" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a> <a id="10560" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10562" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="10565" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="10566" class="Symbol">)</a> <a id="10568" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10570" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="10584" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10586" class="Symbol">(</a><a id="10587" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="10590" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="10592" href="Category.Ambient.html#2115" class="Function">idC</a><a id="10595" class="Symbol">)</a>
|
|||
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<a id="10607" href="Monad.Instance.K.Commutative.html#10607" class="Function">by-uni</a> <a id="10614" class="Symbol">:</a> <a id="10616" class="Symbol">(</a><a id="10617" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="10621" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="10624" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="10626" class="Symbol">)</a> <a id="10628" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10630" class="Symbol">(</a><a id="10631" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="10635" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="10638" href="Category.Ambient.html#11055" class="Function">∇</a><a id="10639" class="Symbol">)</a> <a id="10641" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10643" href="Monad.Instance.K.Commutative.html#10504" class="Function">h</a> <a id="10645" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="10647" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="10650" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10652" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a>
|
|||
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|
<a id="10665" href="Monad.Instance.K.Commutative.html#10607" class="Function">by-uni</a> <a id="10672" class="Symbol">=</a> <a id="10674" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
|||
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<a id="10693" class="Symbol">(</a><a id="10694" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="10698" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="10701" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="10703" class="Symbol">)</a> <a id="10705" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10707" class="Symbol">(</a><a id="10708" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="10712" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="10715" href="Category.Ambient.html#11055" class="Function">∇</a><a id="10716" class="Symbol">)</a> <a id="10718" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10720" href="Monad.Instance.K.Commutative.html#10504" class="Function">h</a> <a id="10806" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="10809" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="10815" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="10821" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="10823" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="10829" class="Symbol">(</a><a id="10830" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="10836" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="10838" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="10847" class="Symbol">(</a><a id="10848" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="10854" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="10863" class="Symbol">)</a> <a id="10865" class="Symbol">(</a><a id="10866" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="10872" class="Symbol">(</a><a id="10873" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="10879" href="Categories.Category.Cocartesian.html#2662" class="Function">[]∘+₁</a><a id="10884" class="Symbol">)))</a> <a id="10888" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
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<a id="10903" class="Symbol">(</a><a id="10904" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10907" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="10910" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10913" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10915" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="10917" class="Symbol">(</a><a id="10918" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="10922" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10924" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="10926" class="Symbol">)</a> <a id="10928" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="10930" class="Symbol">(</a><a id="10931" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="10935" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10937" class="Symbol">(</a><a id="10938" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="10941" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="10943" href="Category.Ambient.html#2115" class="Function">idC</a><a id="10946" class="Symbol">))</a> <a id="10949" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="10951" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10953" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="10967" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10969" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="10971" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="10975" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="10977" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a> <a id="10979" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10981" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="10984" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="10985" class="Symbol">)</a> <a id="10987" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="10989" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="11003" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11005" class="Symbol">(</a><a id="11006" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="11009" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="11011" href="Category.Ambient.html#2115" class="Function">idC</a><a id="11014" class="Symbol">)</a> <a id="11016" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="11019" class="Symbol">(</a><a id="11020" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="11029" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="11034" class="Symbol">(</a><a id="11035" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="11041" href="Categories.Category.Cocartesian.html#2736" class="Function">∘[]</a> <a id="11045" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="11047" class="Symbol">(</a><a id="11048" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="11057" class="Symbol">(</a><a id="11058" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="11066" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="11075" class="Symbol">)</a> <a id="11077" class="Sym
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<a id="11140" class="Symbol">(</a><a id="11141" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11144" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="11147" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="11149" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11152" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11154" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11157" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="11159" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11162" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11164" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11167" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="11169" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11171" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="11185" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11187" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="11189" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="11193" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="11195" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a> <a id="11197" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11199" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="11202" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="11203" class="Symbol">)</a> <a id="11205" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11207" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="11221" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11223" class="Symbol">(</a><a id="11224" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="11227" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="11229" href="Category.Ambient.html#2115" class="Function">idC</a><a id="11232" class="Symbol">)</a> <a id="11253" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="11256" class="Symbol">(</a><a id="11257" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="11266" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="11271" class="Symbol">(</a><a id="11272" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="11278" class="Symbol">((</a><a id="11280" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="11284" href="Categories.Category.Cocartesian.html#2736" class="Function">∘[]</a><a id="11287" class="Symbol">)</a> <a id="11289" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="11297" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="11299" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="11305" href="Categories.Category.Distributive.Properties.html#1458" class="Function">distributeˡ⁻¹-π₁</a><a id="11321" class="Symbol">)))</a> <a id="11325" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="11333" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="11348" class="Symbol">(</a><a id="11349" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11352" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="11355" class="Symbol">(</a><a id="11356" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11359" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11361" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="11363" class="Symbol">)</a> <a id="11365" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11367" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="11369" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="11373" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="11375" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a> <a id="11377" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11379" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="11382" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="11383" class="Symbol">)</a> <a id="11385" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11387" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="11401" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11403" class="Symbol">(</a><a id="11404" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="11407" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="11409" href="Category.Ambient.html#2115" class="Function">idC</a><a id="11412" class="Symbol">)</a> <a id="11461" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="11464" class="Symbol">(</a><a id="11465" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="11474" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="11479" class="Symbol">(</a><a id="11480" href="Categories.Morphism.Reasoning.Core.html#6665" class="Function">cancelʳ</a> <a id="11488" href="Categories.Object.Product.Core.html#603" class="Function">project₁</a><a id="11496" class="Symbol">))</a> <a id="11499" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="11507" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="11522" class="Symbol">(</a><a id="11523" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11526" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="11529" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="11531" class="Symbol">)</a> <a id="11533" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11535" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="11549" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11551" class="Symbol">(</a><a id="11552" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="11555" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="11557" href="Category.Ambient.html#2115" class="Function">idC</a><a id="11560" class="Symbol">)</a> <a id="11635" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="11638" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="11644" href="Categories.Category.Distributive.Properties.html#1915" class="Function">distributeʳ⁻¹-π₁</a> <a id="11661" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="11676" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11679" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11681" class="Symbol">(</a><a id="11682" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="11685" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="11687" href="Category.Ambient.html#2115" class="Function">idC</a><a id="11690" class="Symbol">)</a> <a id="11789" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="11792" href="Categories.Category.BinaryProducts.html#2391" class="Function">π₁∘⁂</a> <a id="11797" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="11812" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="11815" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11817" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11925" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="11937" href="Monad.Instance.K.Commutative.html#11937" class="Function">step₁</a> <a id="11943" class="Symbol">:</a> <a id="11945" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="11952" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="11954" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="11957" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="11959" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11961" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11964" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="11966" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="11968" class="Symbol">_</a> <a id="11970" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11972" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11975" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="11977" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11979" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="11981" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="11983" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="11985" class="Symbol">(</a><a id="11986" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="11988" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="11991" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11993" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="11996" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="11998" class="Symbol">(</a><a id="11999" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="12002" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="12004" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12006" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="12009" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="12012" href="Category.Ambient.html#2115" class="Function">idC</a><a id="12015" class="Symbol">)</a> <a id="12017" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12019" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="12033" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="12035" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12037" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="12051" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12053" class="Symbol">(</a><a id="12054" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="12057" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="12059" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="12060" class="Symbol">))</a><a id="12062" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
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<a id="12074" href="Monad.Instance.K.Commutative.html#11937" class="Function">step₁</a> <a id="12080" class="Symbol">=</a> <a id="12082" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="12100" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="12107" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="12109" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="12112" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="12114" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12116" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="12119" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="12121" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="12123" class="Symbol">_</a> <a id="12125" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12127" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="12130" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="12132" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12134" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="12136" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="12312" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="12315" href="Monad.Instance.K.Commutative.html#8711" class="Function">extend-preserve</a> <a id="12331" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="12333" class="Symbol">(</a><a id="12334" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="12337" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="12338" class="Symbol">)</a> <a id="12340" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12342" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="12345" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="12347" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="12349" class="Symbol">(</a><a id="12350" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="12354" href="Monad.Instance.K.Commutative.html#9499" class="Bound">Y</a><a id="12355" class="Symbol">)</a> <a id="12357" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12359" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="12362" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="12364" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="12366" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="12381" class="Symbol">((</a><a id="12383" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="12390" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="12392" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="12395" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="12397" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12399" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="12402" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="12404" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="12406" class="Symbol">_</a> <a id="12408" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12410" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="12413" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="12415" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="12418" href="Category.Ambient.html#2115" class="Function">idC</a><a id="12421" class="Symbol">)</a> <a id="12423" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12425" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a><a id="12426" class="Symbol">)</a> <a id="12428" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="12593" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="12596" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="12605" class="Symbol">(</a><a id="12606" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="12615" class="Symbol">_)</a> <a id="12618" class="Symbol">(</a><a id="12619" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="12625" class="Symbol">(</a><a id="12626" href="Categories.Category.Cocartesian.html#2736" class="Function">∘[]</a> <a id="12630" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="12632" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="12641" class="Symbol">(</a><a id="12642" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="12648" href="Categories.Category.Cocartesian.html#2548" class="Function">+₁∘i₁</a><a id="12653" class="Symbol">)</a> <a id="12655" class="Symbol">(</a><a id="12656" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="12662" class="Symbol">(</a><a id="12663" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="12669" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="12671" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="12680" class="Symbol">(</a><a id="12681" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="12687" class="Symbol">(</a><a id="12688" href="Category.Ambient.html#10469" class="Function">extend∘F₁</a> <a id="12698" href="Monad.Instance.K.html#1609" class="Function">monadK</a> <a id="12705" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="12707" class="Symbol">(</a><a id="12708" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="12711" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="12712" class="Symbol">)</a> <a id="12714" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12716" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="12719" href="Categories.Object.Coproduct.html#532" class="Function Operator">,<
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<a id="12800" class="Symbol">(</a><a id="12801" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="12803" class="Symbol">(</a><a id="12804" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="12807" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12809" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="12816" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="12818" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="12821" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="12823" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12825" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="12828" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="12830" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="12832" class="Symbol">_</a> <a id="12834" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12836" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="12839" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="12840" class="Symbol">)</a> <a id="12842" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12844" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="12848" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="12851" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12853" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="12855" class="Symbol">_</a> <a id="12857" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="12859" class="Symbol">((</a><a id="12861" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="12868" class="Symbol">(</a><a id="12869" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="12871" class="Symbol">(</a><a id="12872" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="12876" href="Monad.Instance.K.Commutative.html#9499" class="Bound">Y</a><a id="12877" class="Symbol">)</a> <a id="12879" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12881" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="12883" class="Symbol">)</a> <a id="12885" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12887" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="12889" class="Symbol">_</a> <a id="12891" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="12894" href="Category.Ambient.html#2115" class="Function">idC</a><a id="12897" class="Symbol">))</a> <a id="12900" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12902" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="12916" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12918" class="Symbol">(</a><a id="12919" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="12922" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="12924" href="Category.Ambient.html#2115" class="Function">idC</a><a id="12927" class="Symbol">)</a> <a id="12929" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="12931" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12933" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="12947" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12949" class="Symbol">(</a><a id="12950" href="Category.Ambient.html#2115" class="Fun
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<a id="13271" class="Symbol">(</a><a id="13272" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="13274" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="13277" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13279" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="13286" class="Symbol">(</a><a id="13287" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="13290" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="13292" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13294" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="13296" class="Symbol">)</a> <a id="13298" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13300" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="13302" class="Symbol">_</a> <a id="13304" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="13306" class="Symbol">(</a><a id="13307" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="13311" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="13314" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13316" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="13318" class="Symbol">_</a> <a id="13320" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="13323" href="Category.Ambient.html#2115" class="Function">idC</a><a id="13326" class="Symbol">)</a> <a id="13328" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13330" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="13344" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13346" class="Symbol">(</a><a id="13347" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="13350" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="13352" href="Category.Ambient.html#2115" class="Function">idC</a><a id="13355" class="Symbol">)</a> <a id="13357" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="13359" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13361" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="13375" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13377" class="Symbol">(</a><a id="13378" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="13382" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="13384" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="13386" class="Symbol">))</a> <a id="13389" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="13483" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="13486" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="13495" class="Symbol">(</a><a id="13496" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="13505" class="Symbol">_)</a> <a id="13508" class="Symbol">(</a><a id="13509" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="13517" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="13525" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="13529" class="Symbol">(</a><a id="13530" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="13534" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="13536" href
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<a id="13904" class="Symbol">(</a><a id="13905" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="13907" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="13910" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13912" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="13919" class="Symbol">(</a><a id="13920" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="13923" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="13925" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13927" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="13929" class="Symbol">)</a> <a id="13931" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13933" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="13935" class="Symbol">_</a> <a id="13937" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="13939" class="Symbol">(</a><a id="13940" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="13944" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="13947" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13949" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="13951" class="Symbol">_</a> <a id="13953" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="13956" href="Category.Ambient.html#2115" class="Function">idC</a><a id="13959" class="Symbol">)</a> <a id="13961" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13963" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="13977" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13979" class="Symbol">(</a><a id="13980" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="13983" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="13985" href="Category.Ambient.html#2115" class="Function">idC</a><a id="13988" class="Symbol">)</a> <a id="13990" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="13992" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="13994" class="Symbol">(</a><a id="13995" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="13999" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="14001" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="14003" class="Symbol">_</a> <a id="14005" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="14008" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="14012" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="14014" href="Category.Ambient.html#2115" class="Function">idC</a><a id="14017" class="Symbol">)</a> <a id="14019" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14021" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="14035" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14037" class="Symbol">(</a><a id="14038" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="14042" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="14044" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="14045" class="Symbol">))</a> <a id="14048" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="14116" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="14119" href="Al
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<a id="14227" class="Symbol">(</a><a id="14228" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="14230" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="14233" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14235" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="14242" class="Symbol">(</a><a id="14243" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="14246" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="14248" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14250" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="14252" class="Symbol">)</a> <a id="14254" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14256" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="14258" class="Symbol">_</a> <a id="14260" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14262" class="Symbol">(</a><a id="14263" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="14267" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="14269" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="14271" class="Symbol">_)</a> <a id="14274" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="14276" class="Symbol">(</a><a id="14277" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="14281" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="14284" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14286" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="14288" class="Symbol">_</a> <a id="14290" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="14293" href="Category.Ambient.html#2115" class="Function">idC</a><a id="14296" class="Symbol">)</a> <a id="14298" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14300" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="14314" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14316" class="Symbol">(</a><a id="14317" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="14320" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="14322" href="Category.Ambient.html#2115" class="Function">idC</a><a id="14325" class="Symbol">)</a> <a id="14327" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="14329" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14331" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="14345" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14347" class="Symbol">(</a><a id="14348" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="14352" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="14354" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="14355" class="Symbol">))</a> <a id="14358" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="14439" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="14442" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="14451" class="Symbol">(</a><a id="14452" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="14461" class="Symbol">_)</a> <a id="14464" class="Symbol">((</a><a id="14466" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="14475" class="Symbol">(</a><a
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<a id="14579" class="Symbol">(</a><a id="14580" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="14582" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="14585" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14587" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="14590" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="14592" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14594" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="14597" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="14599" class="Symbol">(</a><a id="14600" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="14603" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="14606" href="Category.Ambient.html#2115" class="Function">idC</a><a id="14609" class="Symbol">)</a> <a id="14611" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14613" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="14627" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14629" class="Symbol">(</a><a id="14630" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="14633" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="14635" href="Category.Ambient.html#2115" class="Function">idC</a><a id="14638" class="Symbol">)</a> <a id="14640" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="14642" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14644" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="14658" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="14660" class="Symbol">(</a><a id="14661" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="14665" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="14667" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="14668" class="Symbol">))</a> <a id="14671" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="14791" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="14794" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="14803" class="Symbol">(</a><a id="14804" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="14813" class="Symbol">_)</a> <a id="14816" class="Symbol">((</a><a id="14818" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="14827" class="Symbol">(</a><a id="14828" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="14836" class="Symbol">((</a><a id="14838" href="Algebra.Elgot.html#2011" class="Function">#-Fixpoint</a> <a id="14849" class="Symbol">(</a><a id="14850" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="14859" class="Symbol">_))</a> <a id="14863" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="14871" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="14873" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="14879" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="14881" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="14889" class="Symbol">(</a><a id="14890" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="14894" href="Categories.Category.BinaryProducts.html#2391" class="Function">
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<a id="15225" class="Symbol">(</a><a id="15226" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="15228" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="15231" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15233" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="15235" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15239" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="15241" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="15244" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="15246" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="15248" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15250" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15253" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="15255" class="Symbol">(</a><a id="15256" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15259" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="15262" href="Category.Ambient.html#2115" class="Function">idC</a><a id="15265" class="Symbol">)</a> <a id="15267" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15269" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="15283" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="15285" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15287" class="Symbol">((</a><a id="15289" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="15292" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15294" href="Category.Ambient.html#2115" class="Function">idC</a><a id="15297" class="Symbol">)</a> <a id="15299" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="15302" class="Symbol">(</a><a id="15303" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="15306" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15308" href="Category.Ambient.html#2115" class="Function">idC</a><a id="15311" class="Symbol">))</a> <a id="15314" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15316" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="15330" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15332" class="Symbol">(</a><a id="15333" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15337" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15339" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="15340" class="Symbol">))</a> <a id="15343" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="15437" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="15440" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="15449" class="Symbol">(</a><a id="15450" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="15459" class="Symbol">_)</a> <a id="15462" class="Symbol">(</a><a id="15463" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="15471" class="Symbol">(</a><a id="15472" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="15478" class="Symbol">(</a><a id="15479" href="Categories.Category.Distributive.Properties.html#3231" class="Function">distributeˡ⁻¹-natural</a> <a id="15501" href
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<a id="15530" class="Symbol">(</a><a id="15531" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="15533" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="15536" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15538" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="15540" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15544" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="15546" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="15549" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="15551" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="15553" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15555" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15558" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="15560" class="Symbol">(</a><a id="15561" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15564" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="15567" href="Category.Ambient.html#2115" class="Function">idC</a><a id="15570" class="Symbol">)</a> <a id="15572" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15574" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="15588" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="15590" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15592" class="Symbol">(</a><a id="15593" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="15607" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15609" class="Symbol">(</a><a id="15610" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="15613" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15615" class="Symbol">(</a><a id="15616" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15620" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="15623" href="Category.Ambient.html#2115" class="Function">idC</a><a id="15626" class="Symbol">)))</a> <a id="15630" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15632" class="Symbol">(</a><a id="15633" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15637" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15639" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="15640" class="Symbol">))</a> <a id="15643" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="15742" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="15745" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="15754" class="Symbol">(</a><a id="15755" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="15764" class="Symbol">_)</a> <a id="15767" class="Symbol">(</a><a id="15768" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="15776" class="Symbol">(</a><a id="15777" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="15783" class="Symbol">(</a><a id="15784" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="15788" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="15790" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="15798" href="Categories.Catego
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<a id="15870" class="Symbol">(</a><a id="15871" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="15873" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="15876" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15878" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="15880" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15884" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="15886" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="15889" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="15891" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="15893" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15895" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15898" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="15900" class="Symbol">(</a><a id="15901" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15904" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="15907" href="Category.Ambient.html#2115" class="Function">idC</a><a id="15910" class="Symbol">)</a> <a id="15912" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15914" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="15928" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="15930" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15932" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="15946" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15948" class="Symbol">(</a><a id="15949" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="15952" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15954" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="15955" class="Symbol">))</a> <a id="15958" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="16082" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="16085" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="16094" class="Symbol">(</a><a id="16095" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="16104" class="Symbol">_)</a> <a id="16107" class="Symbol">((</a><a id="16109" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="16118" class="Symbol">(</a><a id="16119" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="16127" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="16135" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="16139" href="Categories.Category.Distributive.Properties.html#1915" class="Function">distributeʳ⁻¹-π₁</a><a id="16155" class="Symbol">)</a> <a id="16157" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="16161" class="Symbol">)</a> <a id="16163" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="16170" class="Symbol">)</a> <a id="16172" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="16187" class="Symbol">(</a><a id="16188" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="16190" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="16193" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16195" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="16197" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16201" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="16203" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="16206" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="16208" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="16210" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16212" class="Symbol">(</a><a id="16213" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16216" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16219" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="16221" class="Symbol">)</a> <a id="16223" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16225" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="16239" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="16241" class="Symbol">(</a><a id="16242" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16245" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16248" href="Category.Ambient.html#2115" class="Function">idC</a><a id="16251" class="Symbol">)</a> <a id="16253" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16255" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="16269" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="16271" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16273" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="16287" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16289" class="Symbol">(</a><a id="16290" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="16293" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16295" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="16296" class="Symbol">))</a> <a id="16299" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="16399" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="16403" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="16412" class="Symbol">(</a><a id="16413" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="16422" class="Symbol">_)</a> <a id="16425" class="Symbol">(</a><a id="16426" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="16432" class="Symbol">(</a><a id="16433" href="Categories.Category.Cocartesian.html#2662" class="Function">[]∘+₁</a> <a id="16439" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="16441" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="16450" href="Categories.Morphism.Reasoning.Core.html#1551" class="Function">assoc²'</a> <a id="16458" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="16462" class="Symbol">))</a> <a id="16465" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="16480" class="Symbol">(</a><a id="16481" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="16483" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="16486" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16488" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="16490" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16494" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="16496" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="16499" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="16501" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="16503" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16505" class="Symbol">(</a><a id="16506" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16509" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16512" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="16514" class="Symbol">)</a> <a id="16516" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="16518" class="Symbol">(</a><a id="16519" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16522" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16525" href="Category.Ambient.html#2115" class="Function">idC</a><a id="16528" class="Symbol">)</a> <a id="16530" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="16532" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16534" class="Symbol">(</a><a id="16535" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="16549" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16552" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a><a id="16565" class="Symbol">)</a> <a id="16567" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16569" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="16583" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16585" class="Symbol">(</a><a id="16586" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="16589" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16591" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="16592" class="Symbol">))</a> <a id="16595" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="16692" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="16695" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="16704" class="Symbol">(</a><a id="16705" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="16714" class="Symbol">_)</a> <a id="16717" class="Symbol">(</a><a id="16718" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="16726" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="16732" href="Category.Ambient.html#3092" class="Function">distribute₄</a><a id="16743" class="Symbol">)</a> <a id="16745" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="16760" class="Symbol">(</a><a id="16761" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="16763" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="16766" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16768" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="16770" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16774" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="16776" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="16779" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="16781" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="16783" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16785" class="Symbol">(</a><a id="16786" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16789" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16792" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="16794" class="Symbol">)</a> <a id="16796" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="16798" class="Symbol">(</a><a id="16799" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16802" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16805" href="Category.Ambient.html#2115" class="Function">idC</a><a id="16808" class="Symbol">)</a> <a id="16810" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="16812" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16814" class="Symbol">(</a><a id="16815" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="16817" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="16820" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16823" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="16826" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="16828" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a> <a id="16831" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16834" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a> <a id="16837" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="16839" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16841" class="Symbol">(</a><a id="16842" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="16856" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16859" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="16872" class="Symbol">)</a> <a id="16874" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16876" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a><a id="16889" class="Symbol">)</a> <a id="16891" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16893" class="Symbol">(</a><a id="16894" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="16897" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16899" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="16900" class="Symbol">))</a> <a id="16903" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="16972" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="16975" href="Algebra.Elgot.ht
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<a id="17057" class="Symbol">((</a><a id="17059" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="17061" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="17063" class="Symbol">((</a><a id="17065" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="17068" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17070" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="17072" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="17076" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="17078" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="17081" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="17083" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="17085" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17087" class="Symbol">(</a><a id="17088" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17091" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="17094" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="17096" class="Symbol">))</a> <a id="17099" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17101" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a><a id="17103" class="Symbol">)</a> <a id="17105" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="17107" class="Symbol">(((</a><a id="17110" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17113" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="17116" href="Category.Ambient.html#2115" class="Function">idC</a><a id="17119" class="Symbol">))</a> <a id="17122" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17124" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a><a id="17126" class="Symbol">)</a> <a id="17128" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="17130" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="17132" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="17134" class="Symbol">((</a><a id="17136" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="17139" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17141" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="17143" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="17147" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="17149" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="17152" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="17154" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="17156" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17158" class="Symbol">(</a><a id="17159" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17162" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="17165" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="17167" class="Symbol">))</a> <a id="17170" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17172" href="Categories.Object.Coproduct.html#512" class="Function">i₂</a><a id="17174" class="Symbol">)</a> <a id="17176" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="17178" class="Symbol">(((</a><a id="17181" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17184" hre
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<a id="18601" href="Monad.Instance.K.Commutative.html#18601" class="Function">step₂</a> <a id="18607" class="Symbol">:</a> <a id="18609" class="Symbol">(</a><a id="18610" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="18613" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="18614" class="Symbol">)</a> <a id="18616" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18618" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="18621" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="18623" class="Symbol">(</a><a id="18624" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="18626" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="18629" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18631" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="18634" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="18636" class="Symbol">(</a><a id="18637" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="18640" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="18642" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18644" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="18647" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="18650" href="Category.Ambient.html#2115" class="Function">idC</a><a id="18653" class="Symbol">)</a> <a id="18655" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18657" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="18671" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="18673" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18675" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="18689" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18691" class="Symbol">(</a><a id="18692" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="18695" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="18697" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="18698" class="Symbol">))</a><a id="18700" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
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<a id="18712" href="Monad.Instance.K.Commutative.html#18601" class="Function">step₂</a> <a id="18718" class="Symbol">=</a> <a id="18720" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="18739" class="Symbol">(</a><a id="18740" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="18743" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="18744" class="Symbol">)</a> <a id="18746" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18748" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="18873" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="18877" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a> <a id="18890" class="Symbol">(</a><a id="18891" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="18900" class="Symbol">_)</a> <a id="18903" href="Monad.Instance.K.Commutative.html#10607" class="Function">by-uni</a> <a id="18910" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="18925" class="Symbol">((</a><a id="18927" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="18931" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="18934" href="Category.Ambient.html#11055" class="Function">∇</a><a id="18935" class="Symbol">)</a> <a id="18937" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18939" href="Monad.Instance.K.Commutative.html#10504" class="Function">h</a><a id="18940" class="Symbol">)</a><a id="18941" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="19057" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="19060" href="Algebra.Elgot.html#8386" class="Function">#-Diamond</a> <a id="19070" class="Symbol">(</a><a id="19071" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="19080" class="Symbol">_)</a> <a id="19083" href="Monad.Instance.K.Commutative.html#10504" class="Function">h</a> <a id="19085" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="19099" class="Symbol">(</a><a id="19100" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="19102" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="19105" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="19107" class="Symbol">((</a><a id="19109" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19113" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19116" href="Category.Ambient.html#11055" class="Function">∇</a><a id="19117" class="Symbol">)</a> <a id="19119" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19121" href="Monad.Instance.K.Commutative.html#10504" class="Function">h</a><a id="19122" class="Symbol">)</a> <a id="19124" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="19126" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19129" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19133" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="19135" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19137" href="Monad.Instance.K.Commutative.html#10504" class="Function">h</a><a id="19138" class="Symbol">)</a> <a id="19140" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="19231" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="19234" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="19243" class="Symbol">(</a><a id="19244" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="19253" class="Symbol">_)</a> <a id="19256" class="Symbol">((</a><a id="19258" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="19267" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="19272" class="Symbol">(</a><a id="19273" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="19282" class="Symbol">(</a><a id="19283" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a> <a id="19296" class="Symbol">(</a><a id="19297" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="19306" class="Symbol">_)</a> <a id="19309" href="Monad.Instance.K.Commutative.html#10607" class="Function">by-uni</a><a id="19315" class="Symbol">)</a> <a id="19317" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="19321" class="Symbol">))</a> <a id="19324" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="19331" class="Symbol">)</a> <a id="19333" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="19347" class="Symbol">(</a><a id="19348" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="19350" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="19353" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="19355" class="Symbol">(</a><a id="19356" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="19359" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="19361" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19363" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="19365" class="Symbol">)</a> <a id="19367" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19370" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19374" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="19376" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19378" href="Monad.Instance.K.Commutative.html#10504" class="Function">h</a><a id="19379" class="Symbol">)</a> <a id="19381" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="19479" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="19482" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="19491" class="Symbol">(</a><a id="19492" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="19501" class="Symbol">_)</a> <a id="19504" class="Symbol">(</a><a id="19505" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="19511" href="Categories.Category.Cocartesian.html#2662" class="Function">[]∘+₁</a><a id="19516" class="Symbol">)</a> <a id="19518" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="19532" class="Symbol">(</a><a id="19533" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="19535" class="Symbol">(</a><a id="19536" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="19539" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19541" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="19543" class="Symbol">)</a> <a id="19545" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="19547" class="Symbol">(((</a><a id="19550" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="19553" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="19555" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19557" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="19559" class="Symbol">)</a> <a id="19561" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19564" href="Category.Ambient.html#2115" class="Function">idC</a><a id="19567" class="Symbol">)</a> <a id="19569" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19571" class="Symbol">(</a><a id="19572" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="19575" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19578" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="19581" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19583" href="Category.Ambient.html#2115" class="Function">idC</a><a id="19586" class="Symbol">)</a> <a id="19588" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19590" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="19604" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19606" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="19608" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19612" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="19614" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a> <a id="19616" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19618" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="19621" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="19622" class="Symbol">)</a> <a id="19624" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="19626" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19628" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="19642" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19644" class="Symbol">(</a><a id="19645" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="19648" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19650" href="Category.Ambient.html#2115" class="Function">idC</a><a id="19653" class="Symbol">))</a> <a id="19656" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="19664" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="19667" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="19676" class="Symbol">(</a><a id="19677" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="19686" class="Symbol">_)</a> <a id="19689" class="Symbol">((</a><a id="19691" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="19700" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="19705" class="Symbol">(</a><a
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<a id="19772" class="Symbol">(</a><a id="19773" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="19775" class="Symbol">(</a><a id="19776" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="19779" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19781" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="19783" class="Symbol">)</a> <a id="19785" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="19787" class="Symbol">((</a><a id="19789" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="19792" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="19794" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19796" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="19799" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19801" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="19804" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19807" class="Symbol">(</a><a id="19808" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="19811" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19813" href="Category.Ambient.html#2115" class="Function">idC</a><a id="19816" class="Symbol">))</a> <a id="19819" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19821" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="19835" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19837" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="19839" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19843" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="19845" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a> <a id="19847" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19849" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="19852" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="19853" class="Symbol">)</a> <a id="19855" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="19857" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19859" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="19873" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19875" class="Symbol">(</a><a id="19876" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="19879" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19881" href="Category.Ambient.html#2115" class="Function">idC</a><a id="19884" class="Symbol">))</a> <a id="19887" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="19904" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="19908" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="19917" class="Symbol">(</a><a id="19918" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="19927" class="Symbol">_)</a> <a id="19930" class="Symbol">((</a><a id="19932" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="19941" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="19946" class="Symbol">(</a><a id="19947" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="19953" class="Symbol">(</a><a id="19954" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id=
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<a id="20020" class="Symbol">(</a><a id="20021" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="20023" class="Symbol">(</a><a id="20024" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="20027" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20029" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="20031" class="Symbol">)</a> <a id="20033" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="20035" class="Symbol">(</a><a id="20036" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="20039" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="20041" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20043" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="20046" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="20049" href="Category.Ambient.html#2115" class="Function">idC</a><a id="20052" class="Symbol">)</a> <a id="20054" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20056" class="Symbol">((</a><a id="20058" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="20061" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="20063" href="Category.Ambient.html#2115" class="Function">idC</a><a id="20066" class="Symbol">)</a> <a id="20068" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="20071" class="Symbol">(</a><a id="20072" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="20075" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="20077" href="Category.Ambient.html#2115" class="Function">idC</a><a id="20080" class="Symbol">))</a> <a id="20083" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20085" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="20099" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20101" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="20103" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="20107" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="20109" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a> <a id="20111" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20113" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="20116" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="20118" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="20120" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20122" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="20136" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20138" class="Symbol">(</a><a id="20139" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="20142" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="20144" href="Category.Ambient.html#2115" class="Function">idC</a><a id="20147" class="Symbol">))</a> <a id="20150" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="20152" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="20155" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="20164" class="Symbol">(</a><a id="20165" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="20174" class="Symbol">_)</a> <a id="20177" class="Symbol">((</a><a id="20179" href="Categories.Object.Copro
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<a id="21655" class="Symbol">(</a><a id="21656" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="21658" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="21661" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21663" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="21666" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="21668" class="Symbol">(</a><a id="21669" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="21672" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="21674" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21676" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="21679" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21682" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21685" class="Symbol">)</a> <a id="21687" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21689" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="21703" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="21705" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21707" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="21721" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21723" class="Symbol">(</a><a id="21724" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="21726" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21728" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="21730" class="Symbol">))</a><a id="21732" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="21734" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="21737" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="21741" href="Monad.Instance.K.Commutative.html#26642" class="Function">step₂</a> <a id="21747" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="21758" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="21761" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="21763" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21765" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="21768" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a><a id="21769" class="Symbol">)</a>
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<a id="21779" class="Keyword">where</a>
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<a id="21795" href="Monad.Instance.K.Commutative.html#21795" class="Function">h</a> <a id="21797" class="Symbol">=</a> <a id="21799" class="Symbol">(</a><a id="21800" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="21803" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21806" class="Symbol">(</a><a id="21807" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="21810" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21813" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21817" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21819" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="21821" class="Symbol">)</a> <a id="21823" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21825" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="21839" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21841" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="21843" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="21845" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21847" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="21850" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="21852" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21856" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="21857" class="Symbol">)</a> <a id="21859" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21861" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="21875" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21877" class="Symbol">(</a><a id="21878" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21882" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21884" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="21886" class="Symbol">)</a>
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<a id="21898" href="Monad.Instance.K.Commutative.html#21898" class="Function">by-uni</a> <a id="21905" class="Symbol">:</a> <a id="21907" class="Symbol">(</a><a id="21908" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21912" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21915" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="21917" class="Symbol">)</a> <a id="21919" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21921" class="Symbol">(</a><a id="21922" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21926" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21929" href="Category.Ambient.html#11055" class="Function">∇</a><a id="21930" class="Symbol">)</a> <a id="21932" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21934" href="Monad.Instance.K.Commutative.html#21795" class="Function">h</a> <a id="21936" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="21938" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="21941" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21943" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a>
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<a id="21956" href="Monad.Instance.K.Commutative.html#21898" class="Function">by-uni</a> <a id="21963" class="Symbol">=</a> <a id="21965" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="21984" class="Symbol">(</a><a id="21985" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21989" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21992" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="21994" class="Symbol">)</a> <a id="21996" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21998" class="Symbol">(</a><a id="21999" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22003" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="22006" href="Category.Ambient.html#11055" class="Function">∇</a><a id="22007" class="Symbol">)</a> <a id="22009" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22011" href="Monad.Instance.K.Commutative.html#21795" class="Function">h</a> <a id="22097" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="22100" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="22106" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="22112" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="22114" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="22120" class="Symbol">(</a><a id="22121" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="22127" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="22129" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="22138" class="Symbol">(</a><a id="22139" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="22145" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="22154" class="Symbol">)</a> <a id="22156" class="Symbol">(</a><a id="22157" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="22163" class="Symbol">(</a><a id="22164" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="22170" href="Categories.Category.Cocartesian.html#2662" class="Function">[]∘+₁</a><a id="22175" class="Symbol">)))</a> <a id="22179" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="22194" class="Symbol">(</a><a id="22195" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22198" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="22201" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22204" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22206" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="22208" class="Symbol">(</a><a id="22209" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22213" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22215" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="22217" class="Symbol">)</a> <a id="22219" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="22221" class="Symbol">(</a><a id="22222" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22226" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22228" class="Symbol">(</a><a id="22229" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22233" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="22235" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="22237" class="Symbol">))</a> <a id="22240" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="22242" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22244" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="22258" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22260" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="22262" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="22264" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22266" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="22269" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="22271" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22275" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="22276" class="Symbol">)</a> <a id="22278" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22280" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="22294" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22296" class="Symbol">(</a><a id="22297" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22301" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="22303" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="22305" class="Symbol">)</a> <a id="22307" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="22310" class="Symbol">(</a><a id="22311" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="22320" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="22325" class="Symbol">(</a><a id="22326" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="22332" href="Categories.Category.Cocartesian.html#2736" class="Function">∘[]</a> <a id="22336" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="22338" class="Symbol">(</a><a id="22339" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="22348" class="Symbol">(</a><a id="22349" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="22357" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="22366" class="Symbol">)</a> <a id="22368" class="Sym
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<a id="22431" class="Symbol">(</a><a id="22432" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22435" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="22438" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="22440" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22443" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22445" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22448" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="22450" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22453" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22455" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22458" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="22460" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22462" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="22476" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22478" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="22480" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="22482" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22484" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="22487" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="22489" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22493" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="22494" class="Symbol">)</a> <a id="22496" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22498" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="22512" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22514" class="Symbol">(</a><a id="22515" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22519" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="22521" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="22523" class="Symbol">)</a> <a id="22544" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="22547" class="Symbol">(</a><a id="22548" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="22557" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="22562" class="Symbol">(</a><a id="22563" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="22569" class="Symbol">((</a><a id="22571" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="22575" href="Categories.Category.Cocartesian.html#2736" class="Function">∘[]</a><a id="22578" class="Symbol">)</a> <a id="22580" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="22588" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="22590" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="22596" href="Categories.Category.Distributive.Properties.html#2746" class="Function">distributeʳ⁻¹-π₂</a><a id="22612" class="Symbol">)))</a> <a id="22616" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="22624" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="22639" class="Symbol">(</a><a id="22640" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22643" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="22646" class="Symbol">(</a><a id="22647" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22650" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22652" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="22654" class="Symbol">)</a> <a id="22656" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22658" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="22660" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="22662" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22664" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="22667" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="22669" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22673" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="22674" class="Symbol">)</a> <a id="22676" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22678" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="22692" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22694" class="Symbol">(</a><a id="22695" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22699" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="22701" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="22703" class="Symbol">)</a> <a id="22752" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="22755" class="Symbol">(</a><a id="22756" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="22765" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="22770" class="Symbol">(</a><a id="22771" href="Categories.Morphism.Reasoning.Core.html#6665" class="Function">cancelʳ</a> <a id="22779" href="Categories.Object.Product.Core.html#637" class="Function">project₂</a><a id="22787" class="Symbol">))</a> <a id="22790" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="22798" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="22813" class="Symbol">(</a><a id="22814" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22817" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="22820" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="22822" class="Symbol">)</a> <a id="22824" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22826" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="22840" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22842" class="Symbol">(</a><a id="22843" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22847" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="22849" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="22851" class="Symbol">)</a> <a id="22926" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="22929" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="22935" href="Categories.Category.Distributive.Properties.html#2330" class="Function">distributeˡ⁻¹-π₂</a> <a id="22952" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="22967" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="22970" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22972" class="Symbol">(</a><a id="22973" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="22977" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="22979" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="22981" class="Symbol">)</a> <a id="23080" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="23083" href="Categories.Category.BinaryProducts.html#2453" class="Function">π₂∘⁂</a> <a id="23088" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="23103" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="23106" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23108" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23216" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="23228" href="Monad.Instance.K.Commutative.html#23228" class="Function">step₁</a> <a id="23234" class="Symbol">:</a> <a id="23236" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="23243" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="23245" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="23247" class="Symbol">_</a> <a id="23249" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23251" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23254" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="23256" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="23259" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="23261" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23263" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23266" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="23268" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23270" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="23272" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="23274" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="23276" class="Symbol">(</a><a id="23277" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="23279" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="23282" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23284" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23287" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="23289" class="Symbol">(</a><a id="23290" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="23293" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="23295" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23297" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23300" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="23303" href="Category.Ambient.html#2115" class="Function">idC</a><a id="23306" class="Symbol">)</a> <a id="23308" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23310" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="23324" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="23326" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23328" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="23342" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23344" class="Symbol">(</a><a id="23345" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="23347" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="23349" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="23351" class="Symbol">))</a><a id="23353" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
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<a id="23365" href="Monad.Instance.K.Commutative.html#23228" class="Function">step₁</a> <a id="23371" class="Symbol">=</a> <a id="23373" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
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<a id="23392" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="23399" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="23401" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="23403" class="Symbol">_</a> <a id="23405" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23407" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23410" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="23412" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="23415" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="23417" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23419" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23422" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="23424" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23426" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="23428" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="23550" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="23553" href="Monad.Instance.K.Commutative.html#8711" class="Function">extend-preserve</a> <a id="23569" class="Symbol">_</a> <a id="23571" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="23573" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="23588" class="Symbol">((</a><a id="23590" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="23597" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="23599" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="23601" class="Symbol">_</a> <a id="23603" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23605" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23608" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="23610" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="23613" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="23615" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23617" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23620" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="23622" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="23625" href="Category.Ambient.html#2115" class="Function">idC</a><a id="23628" class="Symbol">)</a> <a id="23630" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23632" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a><a id="23633" class="Symbol">)</a> <a id="23635" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="23746" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="23749" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="23758" class="Symbol">(</a><a id="23759" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="23768" class="Symbol">_)</a> <a id="23771" class="Symbol">(</a><a id="23772" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="23778" class="Symbol">(</a><a id="23779" href="Categories.Category.Cocartesian.html#2736" class="Function">∘[]</a> <a id="23783" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="23785" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="23794" class="Symbol">(</a><a id="23795" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="23801" href="Categories.Category.Cocartesian.html#2548" class="Function">+₁∘i₁</a><a id="23806" class="Symbol">)</a> <a id="23808" class="Symbol">(</a><a id="23809" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="23815" class="Symbol">(</a><a id="23816" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="23822" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="23824" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="23833" class="Symbol">(</a><a id="23834" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="23840" class="Symbol">(</a><a id="23841" href="Category.Ambient.html#10469" class="Function">extend∘F₁</a> <a id="23851" href="Monad.Instance.K.html#1609" class="Function">monadK</a> <a id="23858" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="23860" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="23862" class="Symbol">(</a><a id="23863" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="23867" href="Monad.Instance.K.Commutative.html#9507" class="Bound">U</a><a id="23868" class="Symbol">)</a> <a id="23870" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23872" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23875" href="Categories.Object.Coproduct.html#532" class="Function O
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<a id="23953" class="Symbol">(</a><a id="23954" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="23956" class="Symbol">(</a><a id="23957" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="23960" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23962" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="23969" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="23971" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="23973" class="Symbol">_</a> <a id="23975" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23977" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23980" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="23982" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="23985" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="23987" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23989" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="23992" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="23993" class="Symbol">)</a> <a id="23995" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="23997" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="24001" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="24004" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24006" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="24008" class="Symbol">_</a> <a id="24010" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="24012" class="Symbol">(</a><a id="24013" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="24020" class="Symbol">((</a><a id="24022" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="24025" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="24026" class="Symbol">)</a> <a id="24028" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24030" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="24032" class="Symbol">)</a> <a id="24034" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24036" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="24038" class="Symbol">_</a> <a id="24040" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="24043" href="Category.Ambient.html#2115" class="Function">idC</a><a id="24046" class="Symbol">)</a> <a id="24048" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24050" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="24064" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24066" class="Symbol">(</a><a id="24067" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="24070" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="24072" href="Category.Ambient.html#2115" class="Function">idC</a><a id="24075" class="Symbol">)</a> <a id="24077" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="24079" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24081" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="24095" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24097" class="Symbol">(</a><a id="24098" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="24102" href="Categories.Category.BinaryProducts.html#1465" class="Function Ope
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<a id="24277" class="Symbol">(</a><a id="24278" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="24280" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="24283" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24285" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="24289" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="24292" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24294" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="24296" class="Symbol">_</a> <a id="24298" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="24300" class="Symbol">(</a><a id="24301" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="24308" class="Symbol">(</a><a id="24309" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="24312" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="24314" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24316" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="24318" class="Symbol">)</a> <a id="24320" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24322" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="24324" class="Symbol">_</a> <a id="24326" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="24329" href="Category.Ambient.html#2115" class="Function">idC</a><a id="24332" class="Symbol">)</a> <a id="24334" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24336" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="24350" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24352" class="Symbol">(</a><a id="24353" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="24356" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="24358" href="Category.Ambient.html#2115" class="Function">idC</a><a id="24361" class="Symbol">)</a> <a id="24363" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="24365" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24367" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="24381" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24383" class="Symbol">(</a><a id="24384" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="24388" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="24390" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="24392" class="Symbol">))</a> <a id="24395" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="24435" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="24439" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="24448" class="Symbol">(</a><a id="24449" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="24458" class="Symbol">_)</a> <a id="24461" class="Symbol">((</a><a id="24463" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="24472" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="24477" class="Symbol">(</a><a id="24478" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="24486" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="24494" class="Symbol">(</a><a id="24495" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="24499" href="Categories.Cat
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<a id="24551" class="Symbol">(</a><a id="24552" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="24554" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="24557" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24559" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="24563" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="24566" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24568" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="24570" class="Symbol">_</a> <a id="24572" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="24574" class="Symbol">(</a><a id="24575" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="24582" class="Symbol">(</a><a id="24583" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="24586" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="24588" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24590" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="24592" class="Symbol">)</a> <a id="24594" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24596" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="24598" class="Symbol">_</a> <a id="24600" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="24603" href="Category.Ambient.html#2115" class="Function">idC</a><a id="24606" class="Symbol">)</a> <a id="24608" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24610" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="24624" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24626" class="Symbol">((</a><a id="24628" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="24630" class="Symbol">_</a> <a id="24632" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="24635" href="Category.Ambient.html#2115" class="Function">idC</a><a id="24638" class="Symbol">)</a> <a id="24640" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="24642" href="Category.Ambient.html#2115" class="Function">idC</a><a id="24645" class="Symbol">)</a> <a id="24647" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24649" class="Symbol">(</a><a id="24650" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="24652" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="24654" href="Category.Ambient.html#2115" class="Function">idC</a><a id="24657" class="Symbol">)</a> <a id="24659" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="24661" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24663" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="24677" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="24679" class="Symbol">(</a><a id="24680" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="24684" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="24686" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="24688" class="Symbol">))</a> <a id="24691" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="24709" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="24712" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="24721" class="Symbol">(</a><a id="24722" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="24731" class="
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<a id="25150" class="Symbol">(</a><a id="25151" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="25153" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="25156" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25158" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="25162" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="25165" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25167" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="25169" class="Symbol">_</a> <a id="25171" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="25173" class="Symbol">(</a><a id="25174" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="25181" class="Symbol">(</a><a id="25182" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="25185" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="25187" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25189" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="25191" class="Symbol">)</a> <a id="25193" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25195" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="25197" class="Symbol">_</a> <a id="25199" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="25202" href="Category.Ambient.html#2115" class="Function">idC</a><a id="25205" class="Symbol">)</a> <a id="25207" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25209" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="25223" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25225" class="Symbol">(</a><a id="25226" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="25228" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="25230" href="Category.Ambient.html#2115" class="Function">idC</a><a id="25233" class="Symbol">)</a> <a id="25235" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="25237" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25239" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="25253" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25255" class="Symbol">(</a><a id="25256" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="25260" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="25262" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="25264" class="Symbol">))</a> <a id="25267" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="25308" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="25311" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="25320" class="Symbol">(</a><a id="25321" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="25330" class="Symbol">_)</a> <a id="25333" class="Symbol">((</a><a id="25335" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="25344" class="Symbol">(</a><a id="25345" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="25353" href="Monad.Instance.K.Strong.html#3453" class="Function">τ-π₂</a> <a id="25358" class="Symbol">_)</a> <a id="25361" class="Symbol">((</a><a id="25363" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="25372" href="Categories.Monad.Relative.html#953" class="Function">kleisliK.identityʳ</a> <a id="2
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<a id="25431" class="Symbol">(</a><a id="25432" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="25434" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="25437" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25439" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="25442" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="25444" class="Symbol">(</a><a id="25445" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="25448" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="25450" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25452" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="25455" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="25458" href="Category.Ambient.html#2115" class="Function">idC</a><a id="25461" class="Symbol">)</a> <a id="25463" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25465" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="25479" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25481" class="Symbol">(</a><a id="25482" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="25484" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="25486" href="Category.Ambient.html#2115" class="Function">idC</a><a id="25489" class="Symbol">)</a> <a id="25491" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="25493" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25495" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="25509" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="25511" class="Symbol">(</a><a id="25512" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="25516" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="25518" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="25520" class="Symbol">))</a> <a id="25523" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="25589" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="25592" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="25601" class="Symbol">(</a><a id="25602" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="25611" class="Symbol">_)</a> <a id="25614" class="Symbol">((</a><a id="25616" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="25625" class="Symbol">(</a><a id="25626" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="25634" class="Symbol">(</a><a id="25635" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="25639" class="Symbol">(</a><a id="25640" href="Categories.Category.BinaryProducts.html#2453" class="Function">π₂∘⁂</a> <a id="25645" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="25647" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="25656" class="Symbol">)))</a> <a id="25660" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="25664" class="Symbol">)</a> <a id="25666" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="25673" class="Symbol">)</a> <a id="25675" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="26186" class="Symbol">(</a><a id="26187" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="26189" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="26192" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26194" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="26197" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="26199" class="Symbol">(</a><a id="26200" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="26203" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="26205" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26207" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="26210" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="26213" href="Category.Ambient.html#2115" class="Function">idC</a><a id="26216" class="Symbol">)</a> <a id="26218" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26220" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="26234" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="26236" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26238" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="26252" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26254" class="Symbol">(</a><a id="26255" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="26257" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="26259" class="Symbol">(</a><a id="26260" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="26264" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="26267" href="Category.Ambient.html#2115" class="Function">idC</a><a id="26270" class="Symbol">))</a> <a id="26273" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26275" class="Symbol">(</a><a id="26276" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="26280" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="26282" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="26284" class="Symbol">))</a> <a id="26287" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="26344" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="26347" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="26356" class="Symbol">(</a><a id="26357" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="26366" class="Symbol">_)</a> <a id="26369" class="Symbol">(</a><a id="26370" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="26378" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="26386" class="Symbol">(</a><a id="26387" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="26391" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="26393" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="26401" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a> <a id="26411" class="Symbol">(</a><a id="26412" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="26418" class="Symbol">(</a><a id="26419" href="Category.Ambient.html#2218" class="Function">[]-unique</a> <a id="26429" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a> <a id="26441" href="Categories.Morphism.Reasoning.Core.ht
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<a id="26472" class="Symbol">(</a><a id="26473" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="26475" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="26478" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26480" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="26483" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="26485" class="Symbol">(</a><a id="26486" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="26489" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="26491" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26493" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="26496" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="26499" href="Category.Ambient.html#2115" class="Function">idC</a><a id="26502" class="Symbol">)</a> <a id="26504" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26506" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="26520" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="26522" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26524" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="26538" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26540" class="Symbol">(</a><a id="26541" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="26543" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="26545" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="26547" class="Symbol">))</a> <a id="26550" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="26630" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="26642" href="Monad.Instance.K.Commutative.html#26642" class="Function">step₂</a> <a id="26648" class="Symbol">:</a> <a id="26650" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="26653" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="26655" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26657" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="26660" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="26662" class="Symbol">(</a><a id="26663" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="26665" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="26668" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26670" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="26673" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="26675" class="Symbol">(</a><a id="26676" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="26679" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="26681" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26683" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="26686" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="26689" href="Category.Ambient.html#2115" class="Function">idC</a><a id="26692" class="Symbol">)</a> <a id="26694" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26696" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="26710" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="26712" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26714" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="26728" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26730" class="Symbol">(</a><a id="26731" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="26733" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="26735" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="26737" class="Symbol">))</a><a id="26739" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
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<a id="26751" href="Monad.Instance.K.Commutative.html#26642" class="Function">step₂</a> <a id="26757" class="Symbol">=</a> <a id="26759" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="26778" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="26781" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="26783" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26785" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="26910" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="26914" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a> <a id="26927" class="Symbol">(</a><a id="26928" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="26937" class="Symbol">_)</a> <a id="26940" href="Monad.Instance.K.Commutative.html#21898" class="Function">by-uni</a> <a id="26947" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="26962" class="Symbol">((</a><a id="26964" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="26968" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="26971" href="Category.Ambient.html#11055" class="Function">∇</a><a id="26972" class="Symbol">)</a> <a id="26974" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="26976" href="Monad.Instance.K.Commutative.html#21795" class="Function">h</a><a id="26977" class="Symbol">)</a> <a id="26979" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="27094" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="27097" href="Algebra.Elgot.html#8386" class="Function">#-Diamond</a> <a id="27107" class="Symbol">(</a><a id="27108" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="27117" class="Symbol">_)</a> <a id="27120" href="Monad.Instance.K.Commutative.html#21795" class="Function">h</a> <a id="27122" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="27136" class="Symbol">(</a><a id="27137" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="27139" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="27142" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="27144" class="Symbol">((</a><a id="27146" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="27150" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="27153" href="Category.Ambient.html#11055" class="Function">∇</a><a id="27154" class="Symbol">)</a> <a id="27156" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27158" href="Monad.Instance.K.Commutative.html#21795" class="Function">h</a><a id="27159" class="Symbol">)</a> <a id="27161" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="27163" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="27166" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="27170" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="27172" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27174" href="Monad.Instance.K.Commutative.html#21795" class="Function">h</a><a id="27175" class="Symbol">)</a> <a id="27177" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="27268" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="27271" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="27280" class="Symbol">(</a><a id="27281" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="27290" class="Symbol">_)</a> <a id="27293" class="Symbol">((</a><a id="27295" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="27304" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="27309" class="Symbol">(</a><a id="27310" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="27319" class="Symbol">(</a><a id="27320" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a> <a id="27333" class="Symbol">(</a><a id="27334" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="27343" class="Symbol">_)</a> <a id="27346" href="Monad.Instance.K.Commutative.html#21898" class="Function">by-uni</a><a id="27352" class="Symbol">)</a> <a id="27354" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="27358" class="Symbol">))</a> <a id="27361" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="27368" class="Symbol">)</a> <a id="27370" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="27385" class="Symbol">(</a><a id="27386" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="27388" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="27391" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="27393" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="27396" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="27398" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27400" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="27403" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="27406" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="27410" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="27412" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27414" href="Monad.Instance.K.Commutative.html#21795" class="Function">h</a><a id="27415" class="Symbol">)</a> <a id="27417" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="27517" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="27520" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="27529" class="Symbol">(</a><a id="27530" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="27539" class="Symbol">_)</a> <a id="27542" class="Symbol">(</a><a id="27543" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="27549" href="Categories.Category.Cocartesian.html#2662" class="Function">[]∘+₁</a><a id="27554" class="Symbol">)</a> <a id="27556" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="27571" class="Symbol">(</a><a id="27572" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="27574" class="Symbol">(</a><a id="27575" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="27578" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27580" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="27582" class="Symbol">)</a> <a id="27584" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="27586" class="Symbol">(((</a><a id="27589" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="27592" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="27594" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27596" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="27598" class="Symbol">)</a> <a id="27600" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="27603" href="Category.Ambient.html#2115" class="Function">idC</a><a id="27606" class="Symbol">)</a> <a id="27608" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27610" class="Symbol">(</a><a id="27611" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="27614" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="27617" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="27621" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="27623" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="27625" class="Symbol">)</a> <a id="27627" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27629" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="27643" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27645" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="27647" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="27649" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27651" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="27654" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="27656" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="27660" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="27661" class="Symbol">)</a> <a id="27663" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="27665" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27667" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="27681" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="27683" class="Symbol">(</a><a id="27684" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="27688" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="27690" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="27692" class="Symbol">))</a> <a id="27695" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="27703" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="27706" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="27715" class="Symbol">(</a><a id="27716" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="27725" class="Symbol">_)</a> <a id="27728" class="Symbol">((</a><a id="27730" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="27739" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="27744" class="Symbol">(</a><a
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<a id="29144" class="Symbol">(</a><a id="29145" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="29147" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="29150" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29152" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="29155" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="29157" class="Symbol">(</a><a id="29158" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="29161" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29163" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29165" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="29168" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="29171" href="Category.Ambient.html#2115" class="Function">idC</a><a id="29174" class="Symbol">)</a> <a id="29176" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29178" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="29192" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="29194" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29196" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="29210" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29212" class="Symbol">(</a><a id="29213" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="29215" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="29217" class="Symbol">(</a><a id="29218" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="29222" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="29225" href="Category.Ambient.html#2115" class="Function">idC</a><a id="29228" class="Symbol">))</a> <a id="29231" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29233" class="Symbol">(</a><a id="29234" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="29238" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="29240" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="29242" class="Symbol">))</a><a id="29244" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29276" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="29280" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="29289" class="Symbol">(</a><a id="29290" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="29299" class="Symbol">_)</a> <a id="29302" class="Symbol">(</a><a id="29303" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="29311" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="29319" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="29323" class="Symbol">(</a><a id="29324" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="29328" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="29330" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="29338" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a> <a id="29348" class="Symbol">(</a><a id="29349" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="29355" class="Symbol">(</a><a id="29356" href="Category.Ambient.html#2218" class="Function">[]-unique</a> <a id="29366" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a
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<a id="29409" class="Symbol">(</a><a id="29410" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="29412" href="Categories.Object.Coproduct.html#492" class="Function">i₁</a> <a id="29415" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29417" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="29420" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="29422" class="Symbol">(</a><a id="29423" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="29426" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29428" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29430" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="29433" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="29436" href="Category.Ambient.html#2115" class="Function">idC</a><a id="29439" class="Symbol">)</a> <a id="29441" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29443" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="29457" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="29459" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29461" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="29475" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29477" class="Symbol">(</a><a id="29478" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a> <a id="29480" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="29482" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a><a id="29484" class="Symbol">))</a><a id="29486" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29541" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="29549" href="Monad.Instance.K.Commutative.html#29549" class="Function">τσ</a> <a id="29552" class="Symbol">:</a> <a id="29554" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="29561" class="Symbol">(</a><a id="29562" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="29564" class="Symbol">_)</a> <a id="29567" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29569" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="29571" class="Symbol">_</a> <a id="29573" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29575" class="Symbol">(</a><a id="29576" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="29579" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29581" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="29583" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="29586" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="29587" class="Symbol">)</a> <a id="29589" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="29591" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="29598" class="Symbol">(</a><a id="29599" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="29601" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="29603" class="Symbol">_</a> <a id="29605" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29607" class="Symbol">(</a> <a id="29609" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="29612" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29614" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="29616" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="29620" class="Symbol">)</a> <a id="29622" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="29624" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="29626" class="Symbol">_</a> <a id="29628" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29630" class="Symbol">(</a><a id="29631" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="29635" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="29637" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="29640" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="29641" class="Symbol">)</a> <a id="29643" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="29644" class="Symbol">)</a> <a id="29646" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29648" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="29650" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
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<a id="29658" href="Monad.Instance.K.Commutative.html#29549" class="Function">τσ</a> <a id="29661" class="Symbol">=</a> <a id="29663" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="29677" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="29684" class="Symbol">(</a><a id="29685" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="29687" class="Symbol">_)</a> <a id="29690" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29692" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="29694" class="Symbol">_</a> <a id="29696" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29698" class="Symbol">(</a><a id="29699" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="29702" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29704" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="29706" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="29709" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="29710" class="Symbol">)</a> <a id="29823" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="29826" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="29834" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="29842" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="29851" href="Monad.Instance.K.Commutative.html#9946" class="Function">w-law₁</a> <a id="29858" href="Monad.Instance.K.Commutative.html#21503" class="Function">w-law₂</a> <a id="29865" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="29876" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="29883" class="Symbol">(</a><a id="29884" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="29886" class="Symbol">_)</a> <a id="29889" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29891" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="29893" class="Symbol">_</a> <a id="29895" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29897" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="29899" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="29906" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="29908" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="29911" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29913" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29915" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="29918" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="29920" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="29922" class="Symbol">_</a> <a id="29924" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29926" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="29929" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="29931" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29933" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="29935" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29937" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="29939" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="29946" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="29948" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="29950" class="Symbol">_</a> <a id="29952" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29954" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="29957" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="29959" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="29962" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29964" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29966" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="29969" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="29971" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="29973" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="29975" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="29977" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="30022" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="30025" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="30033" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="30041" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="30045" href="Categories.Category.BinaryProducts.html#2599" class="Function">⁂∘⟨⟩</a> <a id="30050" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="30061" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="30068" class="Symbol">(</a><a id="30069" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="30071" class="Symbol">_)</a> <a id="30074" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="30076" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="30078" class="Symbol">_</a> <a id="30080" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="30082" class="Symbol">(</a><a id="30083" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="30090" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="30092" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="30095" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="30097" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="30099" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="30102" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="30104" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="30106" class="Symbol">_</a> <a id="30108" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="30110" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="30113" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="30115" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="30117" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="30124" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="30126" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="30128" class="Symbol">_</a> <a id="30130" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="30132" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="30135" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="30137" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="30140" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="30142" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="30144" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="30147" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="30148" class="Symbol">)</a> <a id="30150" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="30152" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="30154" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="30156" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="30158" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="30160" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="30162" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="30164" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="30207" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="30210" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="30218" class="Symbol">(</a><a id="30219" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="30225" class="Symbol">(</a><a id="30226" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="30230" class="Symbol">(</a><a id="30231" href="Monad.Instance.K.Commutative.html#6892" class="Function">σ-kleisli-assoc</a> <a id="30247" href="Categori
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<a id="33319" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="33326" class="Symbol">(</a><a id="33327" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="33329" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="33336" class="Symbol">(</a><a id="33337" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="33339" class="Symbol">_)</a> <a id="33342" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33344" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="33346" class="Symbol">_</a> <a id="33348" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33350" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="33352" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="33355" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="33357" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33359" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="33362" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="33364" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="33366" class="Symbol">_</a> <a id="33368" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33370" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="33373" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="33375" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="33377" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="33384" class="Symbol">(</a><a id="33385" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="33387" class="Symbol">_)</a> <a id="33390" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33392" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="33394" class="Symbol">_</a> <a id="33396" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33398" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="33400" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="33402" class="Symbol">_</a> <a id="33404" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33406" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="33409" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="33411" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="33414" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="33416" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33418" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="33421" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="33423" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="33424" class="Symbol">)</a> <a id="33426" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33428" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="33430" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="33465" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="33469" class="Symbol">(</a><a id="33470" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="33488" class="Symbol">(</a><a id="33489" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="33498" class="Symbol">(</a><a id="33499" href="Ca
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<a id="33671" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="33678" class="Symbol">(</a><a id="33679" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="33681" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="33688" class="Symbol">(</a><a id="33689" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="33691" class="Symbol">_)</a> <a id="33694" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33696" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="33698" class="Symbol">_</a> <a id="33700" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33702" class="Symbol">(</a><a id="33703" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="33707" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="33709" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="33711" class="Symbol">_)</a> <a id="33714" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33716" class="Symbol">(</a> <a id="33718" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="33721" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="33723" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="33725" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="33729" class="Symbol">)</a> <a id="33731" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="33733" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="33740" class="Symbol">(</a><a id="33741" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="33743" class="Symbol">_)</a> <a id="33746" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33748" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="33750" class="Symbol">_</a> <a id="33752" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33754" class="Symbol">(</a><a id="33755" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="33757" class="Symbol">_</a> <a id="33759" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="33761" href="Category.Ambient.html#2115" class="Function">idC</a><a id="33764" class="Symbol">)</a> <a id="33766" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33768" class="Symbol">(</a><a id="33769" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="33773" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="33775" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="33778" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="33779" class="Symbol">)</a> <a id="33781" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="33782" class="Symbol">)</a> <a id="33784" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="33786" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="33788" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="33817" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="33821" class="Symbol">(</a><a id="33822" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="33840" class="Symbol">(</a><a id="33841" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="33850" class="Symbol">(</a><a id="33851" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="33859" class="Symbol">(</a><a id="33860" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pull
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<a id="34267" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="34274" class="Symbol">(</a><a id="34275" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="34277" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="34284" class="Symbol">(</a><a id="34285" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="34287" class="Symbol">_</a> <a id="34289" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34291" class="Symbol">(</a><a id="34292" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="34296" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="34298" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="34300" class="Symbol">_))</a> <a id="34304" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34306" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="34308" class="Symbol">_</a> <a id="34310" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34312" class="Symbol">(</a> <a id="34314" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="34317" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="34319" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="34321" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="34325" class="Symbol">)</a> <a id="34327" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="34329" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="34331" class="Symbol">_</a> <a id="34333" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34335" class="Symbol">(</a><a id="34336" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="34340" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="34342" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="34345" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="34346" class="Symbol">)</a> <a id="34348" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="34349" class="Symbol">)</a> <a id="34351" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34353" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="34355" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="34413" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="34416" class="Symbol">(</a><a id="34417" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="34435" class="Symbol">(</a><a id="34436" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="34445" class="Symbol">(</a><a id="34446" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="34452" class="Symbol">(</a><a id="34453" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="34471" class="Symbol">(</a><a id="34472" href="Monad.Instance.K.Strong.html#3312" class="Function">τ-η</a> <a id="34476" class="Symbol">_)</a> <a id="34479" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="34481" href="Categories.Monad.Relative.html#1025" class="Function">kleisliK.identityˡ</a><a id="34499" class="Symbol">))</a> <a id="34502" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="34506" class="Symbol">))</a> <a id="34509" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="34517" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="34528" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="34535" class="Symbol">(</a><a id="34536" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="34538" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="34540" class="Symbol">_</a> <a id="34542" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34544" class="Symbol">(</a> <a id="34546" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="34549" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="34551" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="34553" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="34557" class="Symbol">)</a> <a id="34559" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="34561" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="34563" class="Symbol">_</a> <a id="34565" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34567" class="Symbol">(</a><a id="34568" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="34572" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="34574" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="34577" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="34578" class="Symbol">)</a> <a id="34580" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="34581" class="Symbol">)</a> <a id="34583" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34585" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="34587" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="34674" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="34683" href="Monad.Instance.K.Commutative.html#34683" class="Function">στ</a> <a id="34686" class="Symbol">:</a> <a id="34688" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="34695" class="Symbol">(</a><a id="34696" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="34698" class="Symbol">_)</a> <a id="34701" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34703" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="34705" class="Symbol">_</a> <a id="34707" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34709" class="Symbol">(((</a><a id="34712" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="34714" class="Symbol">_</a> <a id="34716" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="34719" href="Category.Ambient.html#2115" class="Function">idC</a><a id="34722" class="Symbol">)</a> <a id="34724" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34726" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a><a id="34727" class="Symbol">)</a> <a id="34729" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="34731" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="34733" class="Symbol">((</a><a id="34735" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="34737" class="Symbol">_</a> <a id="34739" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="34742" href="Category.Ambient.html#2115" class="Function">idC</a><a id="34745" class="Symbol">)</a> <a id="34747" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34749" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="34750" class="Symbol">)</a> <a id="34752" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="34753" class="Symbol">)</a> <a id="34755" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="34757" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="34764" class="Symbol">(</a><a id="34765" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="34767" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="34769" class="Symbol">_</a> <a id="34771" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34773" class="Symbol">(</a> <a id="34775" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="34778" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="34780" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="34782" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="34786" class="Symbol">)</a> <a id="34788" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="34790" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="34792" class="Symbol">_</a> <a id="34794" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34796" class="Symbol">(</a><a id="34797" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="34801" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="34803" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="34806" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="34807" class="Symbol">)</a> <a id="34809" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="34810" class="Symbol">)</a> <a id="34812" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34814" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="34816" href="Monad.Instance.K.Commutative.html#28
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<a id="34824" href="Monad.Instance.K.Commutative.html#34683" class="Function">στ</a> <a id="34827" class="Symbol">=</a> <a id="34829" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="34844" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="34851" class="Symbol">(</a><a id="34852" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="34854" class="Symbol">_)</a> <a id="34857" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34859" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="34861" class="Symbol">_</a> <a id="34863" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34865" class="Symbol">(((</a><a id="34868" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="34870" class="Symbol">_</a> <a id="34872" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="34875" href="Category.Ambient.html#2115" class="Function">idC</a><a id="34878" class="Symbol">)</a> <a id="34880" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34882" href="Monad.Instance.K.Commutative.html#9510" class="Bound">f</a><a id="34883" class="Symbol">)</a> <a id="34885" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="34887" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="34889" class="Symbol">((</a><a id="34891" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="34893" class="Symbol">_</a> <a id="34895" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="34898" href="Category.Ambient.html#2115" class="Function">idC</a><a id="34901" class="Symbol">)</a> <a id="34903" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="34905" href="Monad.Instance.K.Commutative.html#9512" class="Bound">g</a><a id="34906" class="Symbol">)</a> <a id="34908" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="34909" class="Symbol">)</a> <a id="34997" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="35000" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="35008" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="35016" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="35025" href="Monad.Instance.K.Commutative.html#9946" class="Function">w-law₁</a> <a id="35032" href="Monad.Instance.K.Commutative.html#21503" class="Function">w-law₂</a> <a id="35039" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="35050" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35057" class="Symbol">(</a><a id="35058" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="35060" class="Symbol">_)</a> <a id="35063" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35065" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="35067" class="Symbol">_</a> <a id="35069" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35071" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="35073" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35080" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="35082" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="35085" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="35087" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35089" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="35092" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="35094" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="35096" class="Symbol">_</a> <a id="35098" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35100" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="35103" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="35105" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35107" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="35109" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="35111" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="35113" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35120" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="35122" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="35124" class="Symbol">_</a> <a id="35126" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35128" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="35131" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="35133" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="35136" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="35138" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35140" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="35143" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="35145" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35147" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="35149" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="35151" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="35203" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="35206" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="35214" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="35222" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="35226" href="Categories.Category.BinaryProducts.html#2599" class="Function">⁂∘⟨⟩</a> <a id="35231" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="35242" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35249" class="Symbol">(</a><a id="35250" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="35252" class="Symbol">_)</a> <a id="35255" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35257" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="35259" class="Symbol">_</a> <a id="35261" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35263" class="Symbol">(</a><a id="35264" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35271" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="35273" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="35276" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="35278" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35280" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="35283" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="35285" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="35287" class="Symbol">_</a> <a id="35289" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35291" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="35294" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="35296" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="35298" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35305" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="35307" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="35309" class="Symbol">_</a> <a id="35311" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35313" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="35316" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="35318" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="35321" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="35323" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35325" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="35328" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="35329" class="Symbol">)</a> <a id="35331" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35333" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="35335" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="35337" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="35339" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="35341" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="35343" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="35345" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="35395" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="35398" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="35406" class="Symbol">(</a><a id="35407" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="35413" class="Symbol">(</a><a id="35414" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="35418" class="Symbol">(</a><a id="35419" href="Monad.Instance.K.Commutative.html#7643" class="Function">τ-kleisli-assoc</a> <a id="35435" href="C
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<a id="35515" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35522" class="Symbol">(</a><a id="35523" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="35525" class="Symbol">_)</a> <a id="35528" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35530" class="Symbol">(</a><a id="35531" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35538" class="Symbol">(</a><a id="35539" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="35541" class="Symbol">_</a> <a id="35543" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35545" class="Symbol">(</a><a id="35546" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="35550" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="35552" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="35554" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="35556" class="Symbol">(</a><a id="35557" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="35561" href="Monad.Instance.K.Commutative.html#9507" class="Bound">U</a><a id="35562" class="Symbol">)</a> <a id="35564" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35566" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="35569" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="35571" class="Symbol">(</a><a id="35572" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="35575" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="35576" class="Symbol">)</a> <a id="35578" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35580" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="35583" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="35584" class="Symbol">))</a> <a id="35587" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35589" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="35591" class="Symbol">_</a> <a id="35593" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35595" class="Symbol">(</a><a id="35596" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35603" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="35605" class="Symbol">(</a><a id="35606" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="35609" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="35610" class="Symbol">)</a> <a id="35612" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35614" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="35617" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="35619" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="35621" class="Symbol">(</a><a id="35622" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="35626" href="Monad.Instance.K.Commutative.html#9499" class="Bound">Y</a><a id="35627" class="Symbol">)</a> <a id="35629" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35631" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="35634" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="35636" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="35638" href="Category.Ambient.html#2115" class="Function">idC</a><a id="35641" class="Symbol">))</a> <a id="35644" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35646" href="Categories.Category.BinaryProducts.html#1396" class="Function Oper
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<a id="35836" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35843" class="Symbol">(</a><a id="35844" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="35846" class="Symbol">_)</a> <a id="35849" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35851" class="Symbol">(</a><a id="35852" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35859" class="Symbol">(</a><a id="35860" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="35862" class="Symbol">_</a> <a id="35864" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35866" class="Symbol">(</a><a id="35867" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="35871" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="35873" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="35875" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="35877" class="Symbol">(</a><a id="35878" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="35882" href="Monad.Instance.K.Commutative.html#9507" class="Bound">U</a><a id="35883" class="Symbol">)</a> <a id="35885" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35887" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="35890" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="35892" class="Symbol">(</a><a id="35893" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="35896" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="35897" class="Symbol">)</a> <a id="35899" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35901" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="35904" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="35905" class="Symbol">))</a> <a id="35908" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35910" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="35914" class="Symbol">(</a><a id="35915" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="35922" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="35924" class="Symbol">(</a><a id="35925" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="35928" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="35929" class="Symbol">)</a> <a id="35931" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35933" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="35936" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="35938" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="35940" class="Symbol">(</a><a id="35941" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="35945" href="Monad.Instance.K.Commutative.html#9499" class="Bound">Y</a><a id="35946" class="Symbol">)</a> <a id="35948" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35950" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="35953" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="35955" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="35957" href="Category.Ambient.html#2115" class="Function">idC</a><a id="35960" class="Symbol">)</a> <a id="35962" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="35964" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="35966" class="Symbol">_)</a> <a id="35969" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id
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<a id="36046" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="36053" class="Symbol">(</a><a id="36054" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="36056" class="Symbol">_)</a> <a id="36059" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36061" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="36068" class="Symbol">(</a><a id="36069" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="36071" class="Symbol">_</a> <a id="36073" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36075" class="Symbol">(</a><a id="36076" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="36080" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="36082" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="36084" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="36086" class="Symbol">(</a><a id="36087" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="36091" href="Monad.Instance.K.Commutative.html#9507" class="Bound">U</a><a id="36092" class="Symbol">)</a> <a id="36094" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36096" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="36099" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="36101" class="Symbol">(</a><a id="36102" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="36105" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="36106" class="Symbol">)</a> <a id="36108" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36110" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="36113" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="36114" class="Symbol">))</a> <a id="36117" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36119" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="36123" class="Symbol">(</a><a id="36124" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="36131" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="36133" class="Symbol">(</a><a id="36134" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="36137" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="36138" class="Symbol">)</a> <a id="36140" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36142" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="36145" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="36147" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="36149" class="Symbol">(</a><a id="36150" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="36154" href="Monad.Instance.K.Commutative.html#9499" class="Bound">Y</a><a id="36155" class="Symbol">)</a> <a id="36157" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36159" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="36162" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="36164" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="36166" href="Category.Ambient.html#2115" class="Function">idC</a><a id="36169" class="Symbol">)</a> <a id="36171" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36173" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="36175" class="Symbol">_</a> <a id="36177" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36179" href="Categories.Category.
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<a id="36263" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="36270" class="Symbol">(</a><a id="36271" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="36273" class="Symbol">_)</a> <a id="36276" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36278" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="36285" class="Symbol">(</a><a id="36286" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="36288" class="Symbol">_</a> <a id="36290" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36292" class="Symbol">(</a><a id="36293" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="36297" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="36299" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="36301" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="36303" class="Symbol">(</a><a id="36304" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="36308" href="Monad.Instance.K.Commutative.html#9507" class="Bound">U</a><a id="36309" class="Symbol">)</a> <a id="36311" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36313" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="36316" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="36318" class="Symbol">(</a><a id="36319" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="36322" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="36323" class="Symbol">)</a> <a id="36325" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36327" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="36330" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="36331" class="Symbol">))</a> <a id="36334" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36336" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="36340" class="Symbol">(</a><a id="36341" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="36348" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="36350" class="Symbol">(</a><a id="36351" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="36354" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="36355" class="Symbol">)</a> <a id="36357" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36359" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="36362" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="36364" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="36366" class="Symbol">(</a><a id="36367" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="36371" href="Monad.Instance.K.Commutative.html#9499" class="Bound">Y</a><a id="36372" class="Symbol">)</a> <a id="36374" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36376" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="36379" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="36381" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="36383" href="Category.Ambient.html#2115" class="Function">idC</a><a id="36386" class="Symbol">)</a> <a id="36388" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36390" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="36394" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="36396" href="Monad.Instance.K.Commutative.html#2660" cl
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<a id="36505" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="36512" class="Symbol">(</a><a id="36513" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="36515" class="Symbol">_)</a> <a id="36518" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36520" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="36527" class="Symbol">(</a><a id="36528" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="36530" class="Symbol">_</a> <a id="36532" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36534" class="Symbol">(</a><a id="36535" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="36539" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="36541" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="36543" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="36545" class="Symbol">(</a><a id="36546" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="36550" href="Monad.Instance.K.Commutative.html#9507" class="Bound">U</a><a id="36551" class="Symbol">)</a> <a id="36553" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36555" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="36558" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="36560" class="Symbol">(</a><a id="36561" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="36564" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="36565" class="Symbol">)</a> <a id="36567" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36569" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="36572" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="36573" class="Symbol">))</a> <a id="36576" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36578" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="36582" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="36584" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="36591" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="36593" class="Symbol">(</a><a id="36594" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="36597" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="36598" class="Symbol">)</a> <a id="36600" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36602" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="36605" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="36607" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="36609" class="Symbol">(</a><a id="36610" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="36614" href="Monad.Instance.K.Commutative.html#9499" class="Bound">Y</a><a id="36615" class="Symbol">)</a> <a id="36617" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36619" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="36622" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a> <a id="36624" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="36626" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="36628" class="Symbol">_</a> <a id="36630" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="36632" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="36636" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id
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<a id="37903" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="37910" class="Symbol">(</a><a id="37911" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="37913" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="37920" class="Symbol">(</a><a id="37921" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="37923" class="Symbol">_)</a> <a id="37926" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="37928" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="37930" class="Symbol">_</a> <a id="37932" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="37934" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="37936" class="Symbol">(</a><a id="37937" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="37940" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="37941" class="Symbol">)</a> <a id="37943" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="37945" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="37948" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="37950" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="37952" class="Symbol">(</a><a id="37953" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="37957" href="Monad.Instance.K.Commutative.html#9507" class="Bound">U</a><a id="37958" class="Symbol">)</a> <a id="37960" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="37962" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="37965" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="37967" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="37969" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="37976" class="Symbol">(</a><a id="37977" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="37979" class="Symbol">_)</a> <a id="37982" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="37984" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="37986" class="Symbol">_</a> <a id="37988" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="37990" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="37992" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="37994" class="Symbol">(</a><a id="37995" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="37999" href="Monad.Instance.K.Commutative.html#9499" class="Bound">Y</a><a id="38000" class="Symbol">)</a> <a id="38002" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38004" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="38007" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="38009" class="Symbol">(</a><a id="38010" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="38013" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="38014" class="Symbol">)</a> <a id="38016" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38018" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="38021" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="38023" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="38024" class="Symbol">)</a> <a id="38026" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38028" class="Symbol">(</a><a id="38029" href="Monad.Instance.K.Commutative.html#98
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<a id="38260" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="38267" class="Symbol">(</a><a id="38268" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="38270" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="38277" class="Symbol">(</a><a id="38278" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="38280" class="Symbol">_)</a> <a id="38283" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38285" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="38287" class="Symbol">_</a> <a id="38289" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38291" class="Symbol">(</a><a id="38292" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="38296" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="38298" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="38300" class="Symbol">_)</a> <a id="38303" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38305" class="Symbol">(</a> <a id="38307" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="38310" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="38312" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="38314" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="38318" class="Symbol">)</a> <a id="38320" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="38322" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="38329" class="Symbol">(</a><a id="38330" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="38332" class="Symbol">_)</a> <a id="38335" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38337" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="38339" class="Symbol">_</a> <a id="38341" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38343" class="Symbol">(</a><a id="38344" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="38346" class="Symbol">_</a> <a id="38348" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="38350" href="Category.Ambient.html#2115" class="Function">idC</a><a id="38353" class="Symbol">)</a> <a id="38355" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38357" class="Symbol">(</a><a id="38358" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="38362" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="38364" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="38367" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="38368" class="Symbol">)</a> <a id="38370" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="38371" class="Symbol">)</a> <a id="38373" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38375" class="Symbol">(</a><a id="38376" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="38378" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="38379" class="Symbol">)</a> <a id="38413" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="38416" class="Symbol">(</a><a id="38417" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="38435" class="Symbol">(</a><a id="38436" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="38445" class="Symbol">(</a><a id="38446" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="38454" class="Symbol">(</a><a id="38455" hr
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<a id="38596" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="38603" class="Symbol">(</a><a id="38604" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="38606" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="38613" class="Symbol">(</a><a id="38614" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="38616" class="Symbol">_)</a> <a id="38619" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38621" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="38623" class="Symbol">_</a> <a id="38625" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38627" class="Symbol">(</a> <a id="38629" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="38632" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="38634" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="38636" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="38640" class="Symbol">)</a> <a id="38642" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="38644" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="38651" class="Symbol">(</a><a id="38652" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="38654" class="Symbol">_)</a> <a id="38657" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38659" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="38663" class="Symbol">(</a><a id="38664" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="38666" class="Symbol">_</a> <a id="38668" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="38670" href="Category.Ambient.html#2115" class="Function">idC</a><a id="38673" class="Symbol">)</a> <a id="38675" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38677" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="38679" class="Symbol">_</a> <a id="38681" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38683" class="Symbol">(</a><a id="38684" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="38688" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="38690" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="38693" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="38694" class="Symbol">)</a> <a id="38696" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="38697" class="Symbol">)</a> <a id="38699" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38701" class="Symbol">(</a><a id="38702" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="38704" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="38705" class="Symbol">)</a> <a id="38749" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="38752" class="Symbol">(</a><a id="38753" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="38771" class="Symbol">(</a><a id="38772" href="Categories.Object.Coproduct.html#816" class="Function">[]-cong₂</a> <a id="38781" class="Symbol">(</a><a id="38782" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="38788" href="Categories.Monad.Relative.html#953" class="Function">kleisliK.identityʳ</a><a id="38806" class="Symbol">)</a> <a id="38808" class="Symbol">(</a><a id="38809" href="Categories.Morphism.Reasoning.Core.html#6851" class="Function">cancelˡ</a> <a id="38817" class="Symbol">(</a><a id="38818" href="Category.Ambient.html#10469" class="Function">extend∘F₁</
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<a id="38921" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="38928" class="Symbol">(</a><a id="38929" href="Categories.Object.Coproduct.html#532" class="Function Operator">[</a> <a id="38931" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="38933" class="Symbol">_</a> <a id="38935" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38937" class="Symbol">(</a> <a id="38939" href="Monad.Instance.K.Commutative.html#9776" class="Function">f'</a> <a id="38942" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="38944" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="38946" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="38950" class="Symbol">)</a> <a id="38952" href="Categories.Object.Coproduct.html#532" class="Function Operator">,</a> <a id="38954" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="38956" class="Symbol">_</a> <a id="38958" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38960" class="Symbol">(</a><a id="38961" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="38965" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="38967" href="Monad.Instance.K.Commutative.html#9804" class="Function">g'</a> <a id="38970" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="38971" class="Symbol">)</a> <a id="38973" href="Categories.Object.Coproduct.html#532" class="Function Operator">]</a><a id="38974" class="Symbol">)</a> <a id="38976" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="38978" href="Monad.Instance.K.Commutative.html#9832" class="Function">w</a> <a id="38980" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="39074" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="KCommutative"></a><a id="39077" href="Monad.Instance.K.Commutative.html#39077" class="Function">KCommutative</a> <a id="39090" class="Symbol">:</a> <a id="39092" href="Categories.Monad.Commutative.html#715" class="Record">Commutative</a> <a id="39104" class="Symbol">{</a><a id="39105" class="Argument">C</a> <a id="39107" class="Symbol">=</a> <a id="39109" href="Category.Ambient.html#1757" class="Function">C</a><a id="39110" class="Symbol">}</a> <a id="39112" class="Symbol">{</a><a id="39113" class="Argument">V</a> <a id="39115" class="Symbol">=</a> <a id="39117" href="Category.Ambient.html#2297" class="Function">monoidal</a><a id="39125" class="Symbol">}</a> <a id="39127" href="Category.Ambient.html#2445" class="Function">braided</a> <a id="39135" href="Monad.Instance.K.Strong.html#21664" class="Function">KStrong</a>
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<a id="39143" href="Monad.Instance.K.Commutative.html#39077" class="Function">KCommutative</a> <a id="39156" class="Symbol">=</a> <a id="39158" class="Keyword">record</a> <a id="39165" class="Symbol">{</a> <a id="39167" href="Categories.Monad.Commutative.html#1113" class="Field">commutes</a> <a id="39176" class="Symbol">=</a> <a id="39178" href="Monad.Instance.K.Commutative.html#39202" class="Function">commutes'</a> <a id="39188" class="Symbol">}</a>
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<a id="39192" class="Keyword">where</a>
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<a id="39202" href="Monad.Instance.K.Commutative.html#39202" class="Function">commutes'</a> <a id="39212" class="Symbol">:</a> <a id="39214" class="Symbol">∀</a> <a id="39216" class="Symbol">{</a><a id="39217" href="Monad.Instance.K.Commutative.html#39217" class="Bound">X</a> <a id="39219" href="Monad.Instance.K.Commutative.html#39219" class="Bound">Y</a> <a id="39221" class="Symbol">:</a> <a id="39223" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="39226" class="Symbol">}</a> <a id="39228" class="Symbol">→</a> <a id="39230" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39234" class="Symbol">_</a> <a id="39236" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39238" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="39242" class="Symbol">(</a><a id="39243" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39245" class="Symbol">_)</a> <a id="39248" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39250" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="39252" class="Symbol">(</a><a id="39253" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="39257" href="Monad.Instance.K.Commutative.html#39217" class="Bound">X</a> <a id="39259" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="39261" href="Monad.Instance.K.Commutative.html#39219" class="Bound">Y</a><a id="39262" class="Symbol">)</a> <a id="39264" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="39266" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39270" class="Symbol">_</a> <a id="39272" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39274" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="39278" class="Symbol">(</a><a id="39279" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="39281" class="Symbol">_)</a> <a id="39284" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39286" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39288" class="Symbol">_</a>
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<a id="39294" href="Monad.Instance.K.Commutative.html#39202" class="Function">commutes'</a> <a id="39304" class="Symbol">{</a><a id="39305" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a><a id="39306" class="Symbol">}</a> <a id="39308" class="Symbol">{</a><a id="39309" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="39310" class="Symbol">}</a> <a id="39312" class="Symbol">=</a> <a id="39314" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="39327" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39331" class="Symbol">_</a> <a id="39333" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39335" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="39339" class="Symbol">(</a><a id="39340" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39342" class="Symbol">_)</a> <a id="39345" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39347" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="39349" class="Symbol">_</a> <a id="39351" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="39354" href="Algebra.Elgot.Stable.html#3117" class="Field">♯-unique</a> <a id="39363" class="Symbol">(</a><a id="39364" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="39371" class="Symbol">_)</a> <a id="39374" class="Symbol">(</a><a id="39375" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39377" class="Symbol">_)</a> <a id="39380" class="Symbol">(</a><a id="39381" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39385" class="Symbol">(</a><a id="39386" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a> <a id="39388" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="39390" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="39391" class="Symbol">)</a> <a id="39393" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39395" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="39399" class="Symbol">(</a><a id="39400" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39402" class="Symbol">_)</a> <a id="39405" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39407" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="39409" class="Symbol">_)</a> <a id="39412" href="Monad.Instance.K.Commutative.html#39568" class="Function">comm₁</a> <a id="39418" href="Monad.Instance.K.Commutative.html#39940" class="Function">comm₂</a> <a id="39424" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="39433" class="Symbol">(</a><a id="39434" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39436" class="Symbol">_)</a> <a id="39439" href="Monad.Instance.K.Commutative.html#2702" class="Function Operator">♯</a> <a id="39441" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="39444" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="39448" class="Symbol">(</a><a id="39449" href="Algebra.Elgot.Stable.html#3117" class="Field">♯-unique</a> <a id="39458" class="Symbol">(</a><a id="39459" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="39466" class="Symbol">_)</a> <a id="39469" class="Symbol">(</a><a id="39470" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39472" class="Symbol">_)</a> <a id="39475" class="Symbol">(</a><a id="39476" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39480" class="Symbol">_</a> <a id="39482" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39484" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="39488" class="Symbol">(</a><a id="39489" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="39491" class="Symbol">_)</a> <a id="39494" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39496" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39498" class="Symbol">_)</a> <a id="39501" href="Monad.Instance.K.Commutative.html#41154" class="Function">comm₃</a> <a id="39507" href="Monad.Instance.K.Commutative.html#42566" class="Function">comm₄</a><a id="39512" class="Symbol">)</a> <a id="39514" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="39522" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39526" class="Symbol">_</a> <a id="39528" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39530" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="39534" class="Symbol">(</a><a id="39535" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="39537" class="Symbol">_)</a> <a id="39540" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39542" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39544" class="Symbol">_</a> <a id="39546" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="39554" class="Keyword">where</a>
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<a id="39568" href="Monad.Instance.K.Commutative.html#39568" class="Function">comm₁</a> <a id="39574" class="Symbol">:</a> <a id="39576" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39578" class="Symbol">_</a> <a id="39580" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="39582" class="Symbol">(</a><a id="39583" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39587" class="Symbol">_</a> <a id="39589" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39591" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="39595" class="Symbol">(</a><a id="39596" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39598" class="Symbol">_)</a> <a id="39601" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39603" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="39605" class="Symbol">_)</a> <a id="39608" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39610" class="Symbol">(</a><a id="39611" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="39615" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="39617" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="39619" class="Symbol">_)</a>
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<a id="39630" href="Monad.Instance.K.Commutative.html#39568" class="Function">comm₁</a> <a id="39636" class="Symbol">=</a> <a id="39638" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="39642" class="Symbol">(</a><a id="39643" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="39660" class="Symbol">(</a><a id="39661" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39665" class="Symbol">_</a> <a id="39667" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39669" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="39673" class="Symbol">(</a><a id="39674" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39676" class="Symbol">_)</a> <a id="39679" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39681" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="39683" class="Symbol">_)</a> <a id="39686" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39688" class="Symbol">(</a><a id="39689" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="39693" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="39695" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="39697" class="Symbol">_)</a> <a id="39700" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="39703" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="39709" class="Symbol">(</a><a id="39710" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="39716" class="Symbol">(</a><a id="39717" href="Monad.Instance.K.Strong.html#3312" class="Function">τ-η</a> <a id="39721" class="Symbol">_))</a> <a id="39725" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="39738" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39742" class="Symbol">_</a> <a id="39744" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39746" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="39750" class="Symbol">(</a><a id="39751" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39753" class="Symbol">_)</a> <a id="39756" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39758" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="39760" class="Symbol">_</a> <a id="39778" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="39781" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="39789" class="Symbol">(</a><a id="39790" href="Monad.Instance.K.Strong.html#5746" class="Function">K₁η</a> <a id="39794" class="Symbol">_)</a> <a id="39797" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="39809" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39813" class="Symbol">_</a> <a id="39815" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39817" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="39819" class="Symbol">_</a> <a id="39821" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39823" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39825" class="Symbol">_</a> <a id="39849" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="39852" href="Categories.Morphism.Reasoning.Core.html#6851" class="Function">cancelˡ</a> <a id="39860" href="Categories.Monad.html#953" class="Function">monadK.identityʳ</a> <a id="39877" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="39889" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39891" class="Symbol">_</a> <a id="39929" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a><a id="39930" class="Symbol">)</a>
|
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<a id="39940" href="Monad.Instance.K.Commutative.html#39940" class="Function">comm₂</a> <a id="39946" class="Symbol">:</a> <a id="39948" class="Symbol">∀</a> <a id="39950" class="Symbol">{</a><a id="39951" href="Monad.Instance.K.Commutative.html#39951" class="Bound">Z</a> <a id="39953" class="Symbol">:</a> <a id="39955" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="39958" class="Symbol">}</a> <a id="39960" class="Symbol">(</a><a id="39961" href="Monad.Instance.K.Commutative.html#39961" class="Bound">h</a> <a id="39963" class="Symbol">:</a> <a id="39965" href="Monad.Instance.K.Commutative.html#39951" class="Bound">Z</a> <a id="39967" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="39969" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="39973" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a> <a id="39975" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="39977" href="Monad.Instance.K.Commutative.html#39951" class="Bound">Z</a><a id="39978" class="Symbol">)</a> <a id="39980" class="Symbol">→</a> <a id="39982" class="Symbol">(</a><a id="39983" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="39987" class="Symbol">_</a> <a id="39989" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="39991" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="39995" class="Symbol">(</a><a id="39996" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="39998" class="Symbol">_)</a> <a id="40001" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40003" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="40005" class="Symbol">_)</a> <a id="40008" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40010" class="Symbol">(</a><a id="40011" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="40015" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="40017" href="Monad.Instance.K.Commutative.html#39961" class="Bound">h</a> <a id="40019" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="40020" class="Symbol">)</a> <a id="40022" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="40024" class="Symbol">((</a><a id="40026" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="40030" class="Symbol">_</a> <a id="40032" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40034" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="40038" class="Symbol">(</a><a id="40039" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="40041" class="Symbol">_)</a> <a id="40044" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40046" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="40048" class="Symbol">_</a> <a id="40050" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="40053" href="Category.Ambient.html#2115" class="Function">idC</a><a id="40056" class="Symbol">)</a> <a id="40058" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40060" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="40074" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40076" class="Symbol">(</a><a id="40077" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="40081" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="40083" href="Monad.Instance.K.Commutative.html#39961" class="Bound">h</a><a id="40084" class="Symbol">))</a><a id="40086" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
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<a id="40096" href="Monad.Instance.K.Commutative.html#39940" class="Function">comm₂</a> <a id="40102" class="Symbol">{</a><a id="40103" href="Monad.Instance.K.Commutative.html#40103" class="Bound">Z</a><a id="40104" class="Symbol">}</a> <a id="40106" href="Monad.Instance.K.Commutative.html#40106" class="Bound">h</a> <a id="40108" class="Symbol">=</a> <a id="40110" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="40127" class="Symbol">(</a><a id="40128" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="40132" class="Symbol">_</a> <a id="40134" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40136" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="40140" class="Symbol">(</a><a id="40141" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="40143" class="Symbol">_)</a> <a id="40146" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40148" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="40150" class="Symbol">_)</a> <a id="40153" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40155" class="Symbol">(</a><a id="40156" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="40160" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="40162" href="Monad.Instance.K.Commutative.html#40106" class="Bound">h</a> <a id="40164" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="40165" class="Symbol">)</a> <a id="40210" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="40213" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="40219" class="Symbol">(</a><a id="40220" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="40226" class="Symbol">(</a><a id="40227" href="Algebra.Elgot.Stable.html#2892" class="Field">♯-preserving</a> <a id="40240" class="Symbol">(</a><a id="40241" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="40248" class="Symbol">_)</a> <a id="40251" class="Symbol">(</a><a id="40252" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="40254" class="Symbol">_)</a> <a id="40257" href="Monad.Instance.K.Commutative.html#40106" class="Bound">h</a><a id="40258" class="Symbol">))</a> <a id="40261" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="40274" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="40278" class="Symbol">_</a> <a id="40280" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40282" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="40286" class="Symbol">(</a><a id="40287" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="40289" class="Symbol">_)</a> <a id="40292" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40294" class="Symbol">((</a><a id="40296" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="40298" class="Symbol">_</a> <a id="40300" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="40303" href="Category.Ambient.html#2115" class="Function">idC</a><a id="40306" class="Symbol">)</a> <a id="40308" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40310" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="40324" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40326" class="Symbol">(</a><a id="40327" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="40331" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="40333" href="Monad.Instance.K.Commutative.html#40106" class="Bound">h</a><a id="40334" class="Symbol">))</a> <a id="40337" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="40357" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="40360" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="40368" class="Symbol">(</a><a id="40369" href="Category.Construction.ElgotAlgebras.html#812" class="Field">Elgot-Algebra-Morphism.preserves</a> <a id="40402" class="Symbol">((</a><a id="40404" href="Monad.Instance.K.html#1182" class="Field">freealgebras</a> <a id="40417" class="Symbol">_</a> <a id="40419" href="Categories.FreeObjects.Free.html#880" class="Field Operator">FreeObject.*</a><a id="40431" class="Symbol">)</a> <a id="40433" class="Symbol">(</a><a id="40434" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="40436" class="Symbol">_</a> <a id="40438" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40440" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="40442" class="Symbol">_)))</a> <a id="40447" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="40459" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="40463" class="Symbol">_</a> <a id="40465" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40467" class="Symbol">((</a><a id="40469" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="40473" class="Symbol">(</a><a id="40474" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="40476" class="Symbol">_)</a> <a id="40479" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="40482" href="Category.Ambient.html#2115" class="Function">idC</a><a id="40485" class="Symbol">)</a> <a id="40487" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40489" class="Symbol">(</a><a id="40490" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="40492" class="Symbol">_</a> <a id="40494" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="40497" href="Category.Ambient.html#2115" class="Function">idC</a><a id="40500" class="Symbol">)</a> <a id="40502" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40504" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="40518" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40520" class="Symbol">(</a><a id="40521" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="40525" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="40527" href="Monad.Instance.K.Commutative.html#40106" class="Bound">h</a><a id="40528" class="Symbol">))</a> <a id="40531" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="40542" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="40545" href="Category.Construction.ElgotAlgebras.html#812" class="Field">Elgot-Algebra-Morphism.preserves</a> <a id="40578" class="Symbol">(((</a><a id="40581" href="Monad.Instance.K.html#1182" class="Field">freealgebras</a> <a id="40594" class="Symbol">_)</a> <a id="40597" href="Categories.FreeObjects.Free.html#880" class="Field Operator">FreeObject.*</a><a id="40609" class="Symbol">)</a> <a id="40611" href="Category.Ambient.html#2115" class="Function">idC</a><a id="40614" class="Symbol">)</a> <a id="40616" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="40762" class="Symbol">((</a><a id="40764" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="40768" class="Symbol">_</a> <a id="40770" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40772" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="40776" class="Symbol">(</a><a id="40777" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="40779" class="Symbol">_)</a> <a id="40782" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="40785" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="40789" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40791" href="Category.Ambient.html#2115" class="Function">idC</a><a id="40794" class="Symbol">)</a> <a id="40796" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40798" class="Symbol">(</a><a id="40799" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="40801" class="Symbol">_</a> <a id="40803" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="40806" href="Category.Ambient.html#2115" class="Function">idC</a><a id="40809" class="Symbol">)</a> <a id="40811" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40813" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="40827" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40829" class="Symbol">(</a><a id="40830" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="40834" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="40836" href="Monad.Instance.K.Commutative.html#40106" class="Bound">h</a><a id="40837" class="Symbol">))</a> <a id="40840" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="40845" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="40848" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="40857" class="Symbol">(</a><a id="40858" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="40867" class="Symbol">_)</a> <a id="40870" class="Symbol">(</a><a id="40871" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="40877" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a><a id="40882" class="Symbol">)</a> <a id="40884" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="40896" class="Symbol">(((</a><a id="40899" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="40903" class="Symbol">_</a> <a id="40905" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40907" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="40911" class="Symbol">(</a><a id="40912" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="40914" class="Symbol">_))</a> <a id="40918" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40920" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="40922" class="Symbol">_</a> <a id="40924" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="40927" class="Symbol">(</a><a id="40928" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="40932" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40934" href="Category.Ambient.html#2115" class="Function">idC</a><a id="40937" class="Symbol">)</a> <a id="40939" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40941" href="Category.Ambient.html#2115" class="Function">idC</a><a id="40944" class="Symbol">)</a> <a id="40946" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40948" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="40962" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="40964" class="Symbol">(</a><a id="40965" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="40969" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="40971" href="Monad.Instance.K.Commutative.html#40106" class="Bound">h</a><a id="40972" class="Symbol">))</a> <a id="40975" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="40979" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="40982" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="40991" class="Symbol">(</a><a id="40992" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="41001" class="Symbol">_)</a> <a id="41004" class="Symbol">((</a><a id="41006" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="41015" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="41021" class="Symbol">(</a><a id="41022" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="41028" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="41037" class="Symbol">))</a> <a id="41040" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="41047" class="Symbol">)</a> <a id="41049" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="41061" class="Symbol">((</a><a id="41063" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="41067" class="Symbol">_</a> <a id="41069" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41071" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41075" class="Symbol">(</a><a id="41076" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="41078" class="Symbol">_)</a> <a id="41081" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41083" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41085" class="Symbol">_</a> <a id="41087" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="41090" href="Category.Ambient.html#2115" class="Function">idC</a><a id="41093" class="Symbol">)</a> <a id="41095" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41097" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="41111" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41113" class="Symbol">(</a><a id="41114" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="41118" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="41120" href="Monad.Instance.K.Commutative.html#40106" class="Bound">h</a><a id="41121" class="Symbol">))</a><a id="41123" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="41144" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="41154" href="Monad.Instance.K.Commutative.html#41154" class="Function">comm₃</a> <a id="41160" class="Symbol">:</a> <a id="41162" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="41164" class="Symbol">_</a> <a id="41166" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="41168" class="Symbol">(</a><a id="41169" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="41173" class="Symbol">_</a> <a id="41175" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41177" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41181" class="Symbol">(</a><a id="41182" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41184" class="Symbol">_)</a> <a id="41187" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41189" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="41191" class="Symbol">_)</a> <a id="41194" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41196" class="Symbol">(</a><a id="41197" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="41201" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="41203" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="41205" class="Symbol">_)</a>
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<a id="41216" href="Monad.Instance.K.Commutative.html#41154" class="Function">comm₃</a> <a id="41222" class="Symbol">=</a> <a id="41224" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="41228" class="Symbol">(</a><a id="41229" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="41246" class="Symbol">(</a><a id="41247" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="41251" class="Symbol">_</a> <a id="41253" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41255" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41259" class="Symbol">(</a><a id="41260" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41262" class="Symbol">_)</a> <a id="41265" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41267" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="41269" class="Symbol">_)</a> <a id="41272" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41274" class="Symbol">(</a><a id="41275" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="41279" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="41281" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="41283" class="Symbol">_)</a> <a id="41308" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="41311" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="41317" class="Symbol">(</a><a id="41318" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="41324" class="Symbol">(</a><a id="41325" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="41331" class="Symbol">(</a><a id="41332" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="41338" href="Categories.Category.BinaryProducts.html#4512" class="Function">swap∘⁂</a><a id="41344" class="Symbol">)))</a> <a id="41348" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="41361" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="41365" class="Symbol">_</a> <a id="41367" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41369" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41373" class="Symbol">(</a><a id="41374" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41376" class="Symbol">_)</a> <a id="41379" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41381" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41385" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="41390" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41392" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41394" class="Symbol">_</a> <a id="41396" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41398" class="Symbol">(</a><a id="41399" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="41401" class="Symbol">_</a> <a id="41403" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="41405" href="Category.Ambient.html#2115" class="Function">idC</a><a id="41408" class="Symbol">)</a> <a id="41410" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41412" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="41423" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="41426" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41434" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41442" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41450" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41458" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="41466" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="41471" class="Symbol">(</a><a id="41472" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="41476" href="Categories.Functor.Core.html#511" class="Function">K.identity</a><a id="41486" class="Symbol">)</a> <a id="41488" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="41496" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="41509" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="41513" class="Symbol">_</a> <a id="41515" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41517" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41521" class="Symbol">(</a><a id="41522" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41524" class="Symbol">_)</a> <a id="41527" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41529" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41533" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="41538" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41540" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41542" class="Symbol">_</a> <a id="41544" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41546" class="Symbol">(</a><a id="41547" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="41549" class="Symbol">_</a> <a id="41551" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="41553" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41557" href="Category.Ambient.html#2115" class="Function">idC</a><a id="41560" class="Symbol">)</a> <a id="41562" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41564" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="41571" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="41574" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41582" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41590" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41598" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="41604" class="Symbol">(</a><a id="41605" href="Categories.NaturalTransformation.Core.html#827" class="Function">strengthen.commute</a> <a id="41624" class="Symbol">(</a><a id="41625" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="41627" class="Symbol">_</a> <a id="41629" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="41631" href="Category.Ambient.html#2115" class="Function">idC</a><a id="41634" class="Symbol">))</a> <a id="41637" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="41650" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="41654" class="Symbol">_</a> <a id="41656" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41658" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41662" class="Symbol">(</a><a id="41663" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41665" class="Symbol">_)</a> <a id="41668" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41670" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41674" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="41679" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41681" class="Symbol">(</a><a id="41682" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41686" class="Symbol">(</a><a id="41687" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="41689" class="Symbol">_</a> <a id="41691" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="41693" href="Category.Ambient.html#2115" class="Function">idC</a><a id="41696" class="Symbol">)</a> <a id="41698" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41700" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41702" class="Symbol">_)</a> <a id="41705" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41707" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="41712" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="41715" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41723" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41731" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="41737" class="Symbol">(</a><a id="41738" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="41744" class="Symbol">(</a><a id="41745" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="41749" href="Categories.Functor.Core.html#565" class="Function">K.homomorphism</a><a id="41763" class="Symbol">))</a> <a id="41766" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="41779" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="41783" class="Symbol">_</a> <a id="41785" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41787" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41791" class="Symbol">(</a><a id="41792" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41794" class="Symbol">_)</a> <a id="41797" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41799" class="Symbol">(</a><a id="41800" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41804" class="Symbol">(</a><a id="41805" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="41810" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41812" class="Symbol">(</a><a id="41813" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="41815" class="Symbol">_</a> <a id="41817" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="41819" href="Category.Ambient.html#2115" class="Function">idC</a><a id="41822" class="Symbol">))</a> <a id="41825" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41827" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41829" class="Symbol">_)</a> <a id="41832" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41834" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="41841" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="41844" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41852" class="Symbol">(</a><a id="41853" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="41859" class="Symbol">(</a><a id="41860" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="41866" class="Symbol">(</a><a id="41867" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="41871" href="Categories.Functor.Core.html#565" class="Function">K.homomorphism</a><a id="41885" class="Symbol">)))</a> <a id="41889" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="41902" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="41906" class="Symbol">_</a> <a id="41908" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41910" class="Symbol">(</a><a id="41911" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="41915" class="Symbol">(</a><a id="41916" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41918" class="Symbol">_</a> <a id="41920" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41922" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="41927" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41929" class="Symbol">(</a><a id="41930" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="41932" class="Symbol">_</a> <a id="41934" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="41936" href="Category.Ambient.html#2115" class="Function">idC</a><a id="41939" class="Symbol">))</a> <a id="41942" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41944" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="41946" class="Symbol">_)</a> <a id="41949" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="41951" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="41964" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="41967" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41975" class="Symbol">(((</a><a id="41978" href="Categories.Functor.Core.html#696" class="Function">K.F-resp-≈</a> <a id="41989" class="Symbol">(</a><a id="41990" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="41998" href="Categories.Category.BinaryProducts.html#4512" class="Function">swap∘⁂</a><a id="42004" class="Symbol">))</a> <a id="42007" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="42014" class="Symbol">)</a> <a id="42016" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="42023" class="Symbol">)</a> <a id="42025" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="42038" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="42042" class="Symbol">_</a> <a id="42044" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42046" class="Symbol">(</a><a id="42047" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="42051" class="Symbol">(</a><a id="42052" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="42054" class="Symbol">_</a> <a id="42056" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42058" class="Symbol">(</a><a id="42059" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="42063" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="42065" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="42067" class="Symbol">_)</a> <a id="42070" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42072" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="42076" class="Symbol">)</a> <a id="42078" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42080" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="42082" class="Symbol">_)</a> <a id="42085" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42087" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="42100" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="42103" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="42111" class="Symbol">(</a><a id="42112" href="Categories.Functor.Core.html#696" class="Function">K.F-resp-≈</a> <a id="42123" class="Symbol">(</a><a id="42124" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="42130" class="Symbol">(</a><a id="42131" href="Monad.Instance.K.Strong.html#3312" class="Function">τ-η</a> <a id="42135" class="Symbol">_)))</a> <a id="42140" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="42148" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="42156" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="42169" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="42173" class="Symbol">_</a> <a id="42175" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42177" class="Symbol">(</a><a id="42178" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="42182" class="Symbol">(</a><a id="42183" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="42185" class="Symbol">_</a> <a id="42187" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42189" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="42193" class="Symbol">)</a> <a id="42195" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42197" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="42199" class="Symbol">_)</a> <a id="42202" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42204" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="42231" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="42234" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="42242" class="Symbol">((</a><a id="42244" href="Categories.Functor.Core.html#565" class="Function">K.homomorphism</a> <a id="42259" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="42266" class="Symbol">)</a> <a id="42268" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="42275" class="Symbol">)</a> <a id="42277" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="42290" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="42294" class="Symbol">_</a> <a id="42296" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42298" class="Symbol">((</a><a id="42300" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="42304" class="Symbol">(</a><a id="42305" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="42307" class="Symbol">_)</a> <a id="42310" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42312" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="42316" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a><a id="42320" class="Symbol">)</a> <a id="42322" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42324" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="42326" class="Symbol">_)</a> <a id="42329" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42331" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="42352" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="42355" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="42361" class="Symbol">(</a><a id="42362" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="42368" class="Symbol">(</a><a id="42369" href="Categories.Morphism.Reasoning.Core.html#6851" class="Function">cancelˡ</a> <a id="42377" href="Categories.Monad.html#899" class="Function">monadK.identityˡ</a><a id="42393" class="Symbol">))</a> <a id="42396" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="42409" class="Symbol">(</a><a id="42410" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="42414" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="42419" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42421" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="42423" class="Symbol">_)</a> <a id="42426" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42428" href="Categories.Category.BinaryProducts.html#2048" class="Function">swap</a> <a id="42471" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="42474" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="42480" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="42493" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="42495" class="Symbol">_</a> <a id="42555" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a><a id="42556" class="Symbol">)</a>
|
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<a id="42566" href="Monad.Instance.K.Commutative.html#42566" class="Function">comm₄</a> <a id="42572" class="Symbol">:</a> <a id="42574" class="Symbol">∀</a> <a id="42576" class="Symbol">{</a><a id="42577" href="Monad.Instance.K.Commutative.html#42577" class="Bound">Z</a> <a id="42579" class="Symbol">:</a> <a id="42581" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="42584" class="Symbol">}</a> <a id="42586" class="Symbol">(</a><a id="42587" href="Monad.Instance.K.Commutative.html#42587" class="Bound">h</a> <a id="42589" class="Symbol">:</a> <a id="42591" href="Monad.Instance.K.Commutative.html#42577" class="Bound">Z</a> <a id="42593" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="42595" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="42599" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a> <a id="42601" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="42603" href="Monad.Instance.K.Commutative.html#42577" class="Bound">Z</a><a id="42604" class="Symbol">)</a> <a id="42606" class="Symbol">→</a> <a id="42608" class="Symbol">(</a><a id="42609" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="42613" class="Symbol">_</a> <a id="42615" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42617" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="42621" class="Symbol">(</a><a id="42622" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="42624" class="Symbol">_)</a> <a id="42627" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42629" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="42631" class="Symbol">_)</a> <a id="42634" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42636" class="Symbol">(</a><a id="42637" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="42641" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="42643" href="Monad.Instance.K.Commutative.html#42587" class="Bound">h</a> <a id="42645" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="42646" class="Symbol">)</a> <a id="42648" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="42650" class="Symbol">((</a><a id="42652" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="42656" class="Symbol">_</a> <a id="42658" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42660" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="42664" class="Symbol">(</a><a id="42665" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="42667" class="Symbol">_)</a> <a id="42670" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42672" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="42674" class="Symbol">_</a> <a id="42676" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="42679" href="Category.Ambient.html#2115" class="Function">idC</a><a id="42682" class="Symbol">)</a> <a id="42684" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42686" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="42700" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42702" class="Symbol">(</a><a id="42703" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="42707" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="42709" href="Monad.Instance.K.Commutative.html#42587" class="Bound">h</a><a id="42710" class="Symbol">))</a><a id="42712" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
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<a id="42722" href="Monad.Instance.K.Commutative.html#42566" class="Function">comm₄</a> <a id="42728" class="Symbol">{</a><a id="42729" href="Monad.Instance.K.Commutative.html#42729" class="Bound">Z</a><a id="42730" class="Symbol">}</a> <a id="42732" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="42734" class="Symbol">=</a> <a id="42736" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="42753" class="Symbol">(</a><a id="42754" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="42758" class="Symbol">_</a> <a id="42760" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42762" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="42766" class="Symbol">(</a><a id="42767" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="42769" class="Symbol">_)</a> <a id="42772" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42774" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="42776" class="Symbol">_)</a> <a id="42779" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42781" class="Symbol">(</a><a id="42782" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="42786" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="42788" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="42790" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="42791" class="Symbol">)</a> <a id="42817" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="42820" href="Categories.Category.Core.html#1004" class="Function">sym-assoc</a> <a id="42830" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="42838" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="42850" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="42852" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42854" class="Symbol">(</a><a id="42855" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="42859" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="42861" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="42863" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="42864" class="Symbol">)</a> <a id="42914" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="42917" href="Algebra.Elgot.Stable.html#2117" class="Field">♯ˡ-unique</a> <a id="42927" class="Symbol">(</a><a id="42928" href="Monad.Instance.K.Commutative.html#2595" class="Function">stableˡ</a> <a id="42936" class="Symbol">_)</a> <a id="42939" class="Symbol">(</a><a id="42940" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="42942" class="Symbol">(</a><a id="42943" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a> <a id="42945" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="42947" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="42948" class="Symbol">)</a> <a id="42950" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42952" class="Symbol">(</a><a id="42953" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="42957" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="42959" class="Symbol">(</a><a id="42960" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="42962" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="42963" class="Symbol">)))</a> <a id="42967" class="Symbol">(</a><a id="42968" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="42970" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="42972" class="Symbol">(</a><a id="42973" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="42977" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="42979" class="Symbol">(</a><a id="42980" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="42982" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="42983" class="Symbol">)))</a> <a id="42987" class="Symbol">(</a><a id="42988" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="42992" href="Monad.Instance.K.Commutative.html#44217" class="Function">comm₅</a><a id="42997" class="Symbol">)</a> <a id="43000" href="Monad.Instance.K.Commutative.html#46277" class="Function">comm₇</a> <a id="43008" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="43020" class="Symbol">(</a><a id="43021" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="43023" class="Symbol">_</a> <a id="43025" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43027" class="Symbol">(</a><a id="43028" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="43032" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="43034" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="43036" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="43037" class="Symbol">))</a> <a id="43040" href="Monad.Instance.K.Commutative.html#2797" class="Function Operator">♯ˡ</a> <a id="43084" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="43087" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="43091" class="Symbol">(</a><a id="43092" href="Algebra.Elgot.Stable.html#2117" class="Field">♯ˡ-unique</a> <a id="43102" class="Symbol">(</a><a id="43103" href="Monad.Instance.K.Commutative.html#2595" class="Function">stableˡ</a> <a id="43111" class="Symbol">_)</a> <a id="43114" class="Symbol">(</a><a id="43115" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="43117" class="Symbol">(</a><a id="43118" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a> <a id="43120" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="43122" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="43123" class="Symbol">)</a> <a id="43125" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43127" class="Symbol">(</a><a id="43128" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="43132" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="43134" class="Symbol">(</a><a id="43135" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="43137" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="43138" class="Symbol">)))</a> <a id="43142" class="Symbol">(((</a><a id="43145" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="43147" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="43150" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43153" class="Symbol">)</a> <a id="43155" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43157" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="43171" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43173" class="Symbol">(</a><a id="43174" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="43178" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="43180" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="43181" class="Symbol">))</a> <a id="43184" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="43185" class="Symbol">)</a> <a id="43187" class="Symbol">(</a><a id="43188" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="43192" href="Monad.Instance.K.Commutative.html#44700" class="Function">comm₆</a><a id="43197" class="Symbol">)</a> <a id="43199" href="Monad.Instance.K.Commutative.html#48366" class="Function">comm₈</a><a id="43204" class="Symbol">)</a> <a id="43206" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="43218" class="Symbol">((</a><a id="43220" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="43222" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="43225" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43228" class="Symbol">)</a> <a id="43230" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43232" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="43246" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43248" class="Symbol">(</a><a id="43249" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="43253" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="43255" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="43256" class="Symbol">))</a><a id="43258" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="43282" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="43285" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="43294" class="Symbol">(</a><a id="43295" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="43304" class="Symbol">_)</a> <a id="43307" class="Symbol">((</a><a id="43309" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="43318" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="43324" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="43328" class="Symbol">)</a> <a id="43330" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="43337" class="Symbol">)</a> <a id="43340" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="43352" class="Symbol">((</a><a id="43354" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="43358" class="Symbol">_</a> <a id="43360" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43362" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="43366" class="Symbol">(</a><a id="43367" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="43369" class="Symbol">_)</a> <a id="43372" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43374" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="43376" class="Symbol">_</a> <a id="43378" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="43381" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43384" class="Symbol">)</a> <a id="43386" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43388" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="43402" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43404" class="Symbol">(</a><a id="43405" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="43409" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="43411" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="43412" class="Symbol">))</a><a id="43414" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="43416" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="43428" class="Keyword">where</a>
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<a id="43446" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="43448" class="Symbol">:</a> <a id="43450" class="Symbol">∀</a> <a id="43452" class="Symbol">{</a><a id="43453" href="Monad.Instance.K.Commutative.html#43453" class="Bound">X</a> <a id="43455" href="Monad.Instance.K.Commutative.html#43455" class="Bound">Y</a><a id="43456" class="Symbol">}</a> <a id="43458" class="Symbol">→</a> <a id="43460" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="43464" href="Monad.Instance.K.Commutative.html#43453" class="Bound">X</a> <a id="43466" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="43468" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="43472" href="Monad.Instance.K.Commutative.html#43455" class="Bound">Y</a> <a id="43474" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="43476" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="43480" class="Symbol">(</a><a id="43481" href="Monad.Instance.K.Commutative.html#43453" class="Bound">X</a> <a id="43483" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="43485" href="Monad.Instance.K.Commutative.html#43455" class="Bound">Y</a><a id="43486" class="Symbol">)</a>
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<a id="43500" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="43502" class="Symbol">=</a> <a id="43504" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="43511" class="Symbol">(</a><a id="43512" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="43514" class="Symbol">_)</a> <a id="43517" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43519" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="43521" class="Symbol">_</a>
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<a id="43535" href="Monad.Instance.K.Commutative.html#43535" class="Function">ψ-left-iter</a> <a id="43547" class="Symbol">:</a> <a id="43549" class="Symbol">∀</a> <a id="43551" class="Symbol">{</a><a id="43552" href="Monad.Instance.K.Commutative.html#43552" class="Bound">X</a> <a id="43554" href="Monad.Instance.K.Commutative.html#43554" class="Bound">Y</a> <a id="43556" href="Monad.Instance.K.Commutative.html#43556" class="Bound">U</a><a id="43557" class="Symbol">}</a> <a id="43559" class="Symbol">(</a><a id="43560" href="Monad.Instance.K.Commutative.html#43560" class="Bound">h</a> <a id="43562" class="Symbol">:</a> <a id="43564" href="Monad.Instance.K.Commutative.html#43552" class="Bound">X</a> <a id="43566" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="43568" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="43572" href="Monad.Instance.K.Commutative.html#43554" class="Bound">Y</a> <a id="43574" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="43576" href="Monad.Instance.K.Commutative.html#43552" class="Bound">X</a><a id="43577" class="Symbol">)</a> <a id="43579" class="Symbol">→</a> <a id="43581" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="43583" class="Symbol">{</a><a id="43584" href="Monad.Instance.K.Commutative.html#43554" class="Bound">Y</a><a id="43585" class="Symbol">}</a> <a id="43587" class="Symbol">{</a><a id="43588" href="Monad.Instance.K.Commutative.html#43556" class="Bound">U</a><a id="43589" class="Symbol">}</a> <a id="43591" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43593" class="Symbol">(</a><a id="43594" href="Monad.Instance.K.Commutative.html#43560" class="Bound">h</a> <a id="43596" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="43598" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="43600" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43603" class="Symbol">)</a> <a id="43605" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="43607" class="Symbol">((</a><a id="43609" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="43611" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="43614" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43617" class="Symbol">)</a> <a id="43619" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43621" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="43635" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43637" class="Symbol">(</a><a id="43638" href="Monad.Instance.K.Commutative.html#43560" class="Bound">h</a> <a id="43640" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="43642" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43645" class="Symbol">))</a> <a id="43648" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
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<a id="43662" href="Monad.Instance.K.Commutative.html#43535" class="Function">ψ-left-iter</a> <a id="43674" class="Symbol">{</a><a id="43675" href="Monad.Instance.K.Commutative.html#43675" class="Bound">X</a><a id="43676" class="Symbol">}</a> <a id="43678" class="Symbol">{</a><a id="43679" href="Monad.Instance.K.Commutative.html#43679" class="Bound">Y</a><a id="43680" class="Symbol">}</a> <a id="43682" class="Symbol">{</a><a id="43683" href="Monad.Instance.K.Commutative.html#43683" class="Bound">U</a><a id="43684" class="Symbol">}</a> <a id="43686" href="Monad.Instance.K.Commutative.html#43686" class="Bound">h</a> <a id="43688" class="Symbol">=</a> <a id="43690" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="43711" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="43713" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43715" class="Symbol">(</a><a id="43716" href="Monad.Instance.K.Commutative.html#43686" class="Bound">h</a> <a id="43718" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="43720" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="43722" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43725" class="Symbol">)</a> <a id="43779" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="43782" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="43788" class="Symbol">(</a><a id="43789" href="Monad.Instance.K.Commutative.html#3465" class="Function">σ-comm</a> <a id="43796" href="Monad.Instance.K.Commutative.html#43686" class="Bound">h</a><a id="43797" class="Symbol">)</a> <a id="43799" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="43816" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="43823" class="Symbol">(</a><a id="43824" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="43826" class="Symbol">_)</a> <a id="43829" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43831" class="Symbol">((</a><a id="43833" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="43835" class="Symbol">_</a> <a id="43837" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="43840" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43843" class="Symbol">)</a> <a id="43845" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43847" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="43861" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43863" class="Symbol">(</a><a id="43864" href="Monad.Instance.K.Commutative.html#43686" class="Bound">h</a> <a id="43866" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="43868" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43871" class="Symbol">))</a><a id="43873" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="43884" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="43887" href="Monad.Instance.K.Commutative.html#8711" class="Function">extend-preserve</a> <a id="43903" class="Symbol">(</a><a id="43904" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="43906" class="Symbol">(</a><a id="43907" href="Monad.Instance.K.Commutative.html#43679" class="Bound">Y</a> <a id="43909" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="43911" href="Monad.Instance.K.Commutative.html#43683" class="Bound">U</a><a id="43912" class="Symbol">))</a> <a id="43915" class="Symbol">(((</a><a id="43918" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="43920" class="Symbol">_</a> <a id="43922" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="43925" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43928" class="Symbol">)</a> <a id="43930" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43932" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="43946" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="43948" class="Symbol">(</a><a id="43949" href="Monad.Instance.K.Commutative.html#43686" class="Bound">h</a> <a id="43951" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="43953" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43956" class="Symbol">)))</a> <a id="43960" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="43977" class="Symbol">((</a><a id="43979" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="43986" class="Symbol">(</a><a id="43987" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="43989" class="Symbol">_)</a> <a id="43992" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="43995" href="Category.Ambient.html#2115" class="Function">idC</a><a id="43998" class="Symbol">)</a> <a id="44000" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44002" class="Symbol">(</a><a id="44003" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="44005" class="Symbol">_</a> <a id="44007" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="44010" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44013" class="Symbol">)</a> <a id="44015" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44017" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="44031" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44033" class="Symbol">(</a><a id="44034" href="Monad.Instance.K.Commutative.html#43686" class="Bound">h</a> <a id="44036" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44038" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44041" class="Symbol">))</a><a id="44043" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="44045" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="44048" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="44057" class="Symbol">(</a><a id="44058" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="44067" class="Symbol">(</a><a id="44068" href="Monad.Instance.K.Commutative.html#43679" class="Bound">Y</a> <a id="44070" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="44072" href="Monad.Instance.K.Commutative.html#43683" class="Bound">U</a><a id="44073" class="Symbol">))</a> <a id="44076" class="Symbol">(</a><a id="44077" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="44083" class="Symbol">(</a><a id="44084" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="44090" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="44092" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="44101" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="44106" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="44115" class="Symbol">))</a> <a id="44118" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="44135" class="Symbol">(((</a><a id="44138" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="44140" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="44143" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44146" class="Symbol">)</a> <a id="44148" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44150" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="44164" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44166" class="Symbol">(</a><a id="44167" href="Monad.Instance.K.Commutative.html#43686" class="Bound">h</a> <a id="44169" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44171" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44174" class="Symbol">))</a> <a id="44177" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="44178" class="Symbol">)</a> <a id="44203" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="44217" href="Monad.Instance.K.Commutative.html#44217" class="Function">comm₅</a> <a id="44223" class="Symbol">:</a> <a id="44225" class="Symbol">(</a><a id="44226" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="44228" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44230" class="Symbol">(</a><a id="44231" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44235" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44237" class="Symbol">(</a><a id="44238" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="44240" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="44241" class="Symbol">)))</a> <a id="44245" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44247" class="Symbol">(</a><a id="44248" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="44250" class="Symbol">_</a> <a id="44252" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44254" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44257" class="Symbol">)</a> <a id="44259" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="44261" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="44263" class="Symbol">_</a> <a id="44265" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44267" class="Symbol">(</a><a id="44268" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44272" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44274" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="44276" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="44277" class="Symbol">)</a>
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<a id="44291" href="Monad.Instance.K.Commutative.html#44217" class="Function">comm₅</a> <a id="44297" class="Symbol">=</a> <a id="44299" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="44320" class="Symbol">(</a><a id="44321" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="44323" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44325" class="Symbol">(</a><a id="44326" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44330" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44332" class="Symbol">(</a><a id="44333" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="44335" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="44336" class="Symbol">)))</a> <a id="44340" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44342" class="Symbol">(</a><a id="44343" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="44345" class="Symbol">_</a> <a id="44347" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44349" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44352" class="Symbol">)</a> <a id="44356" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="44359" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="44365" class="Symbol">(</a><a id="44366" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="44370" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="44372" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="44380" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a> <a id="44392" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a><a id="44399" class="Symbol">)</a> <a id="44401" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="44418" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="44420" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44422" class="Symbol">(</a><a id="44423" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="44425" class="Symbol">_</a> <a id="44427" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44429" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44433" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44435" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44439" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44441" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="44443" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="44444" class="Symbol">)</a> <a id="44454" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="44457" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="44465" class="Symbol">(</a><a id="44466" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="44470" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a><a id="44473" class="Symbol">)</a> <a id="44475" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="44492" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="44494" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44496" class="Symbol">(</a><a id="44497" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="44499" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a> <a id="44501" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44503" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44506" class="Symbol">)</a> <a id="44508" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44510" class="Symbol">(</a><a id="44511" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44515" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44517" class="Symbol">(</a><a id="44518" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="44520" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="44521" class="Symbol">))</a> <a id="44528" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="44531" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="44537" class="Symbol">(</a><a id="44538" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="44545" href="Monad.Instance.K.Commutative.html#3084" class="Function">σ-η</a> <a id="44550" class="Symbol">)</a> <a id="44552" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
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<a id="44568" class="Symbol">(</a><a id="44569" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="44576" class="Symbol">(</a><a id="44577" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="44579" class="Symbol">_)</a> <a id="44582" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44584" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="44586" class="Symbol">_)</a> <a id="44589" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44591" class="Symbol">(</a><a id="44592" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44596" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44598" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="44600" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="44601" class="Symbol">)</a> <a id="44604" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="44607" href="Categories.Monad.Relative.html#953" class="Function">kleisliK.identityʳ</a> <a id="44626" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="44634" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
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<a id="44650" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="44652" class="Symbol">(</a><a id="44653" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a> <a id="44655" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="44657" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="44658" class="Symbol">)</a> <a id="44660" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44662" class="Symbol">(</a><a id="44663" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44667" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44669" class="Symbol">(</a><a id="44670" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="44672" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="44673" class="Symbol">))</a> <a id="44686" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
|
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<a id="44700" href="Monad.Instance.K.Commutative.html#44700" class="Function">comm₆</a> <a id="44706" class="Symbol">:</a> <a id="44708" class="Symbol">((</a><a id="44710" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="44712" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="44715" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44718" class="Symbol">)</a> <a id="44720" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44722" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="44736" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44738" class="Symbol">(</a><a id="44739" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44743" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44745" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="44746" class="Symbol">))</a><a id="44748" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="44750" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44752" class="Symbol">(</a><a id="44753" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="44755" class="Symbol">_</a> <a id="44757" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44759" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44762" class="Symbol">)</a> <a id="44764" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="44766" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="44768" class="Symbol">_</a> <a id="44770" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44772" class="Symbol">(</a><a id="44773" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44777" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44779" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="44781" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="44782" class="Symbol">)</a>
|
|||
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<a id="44796" href="Monad.Instance.K.Commutative.html#44700" class="Function">comm₆</a> <a id="44802" class="Symbol">=</a> <a id="44804" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
|||
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<a id="44824" class="Symbol">((</a><a id="44826" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="44828" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="44831" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44834" class="Symbol">)</a> <a id="44836" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44838" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="44852" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44854" class="Symbol">(</a><a id="44855" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44859" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44861" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="44862" class="Symbol">))</a> <a id="44865" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="44867" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44869" class="Symbol">(</a><a id="44870" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="44872" class="Symbol">_</a> <a id="44874" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44876" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44879" class="Symbol">)</a> <a id="44881" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="44884" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="44888" class="Symbol">(</a><a id="44889" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a> <a id="44902" class="Symbol">(</a><a id="44903" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="44912" class="Symbol">_)</a> <a id="44915" class="Symbol">(</a><a id="44916" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="44920" href="Monad.Instance.K.Commutative.html#45131" class="Function">by-uni</a><a id="44926" class="Symbol">))</a> <a id="44929" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="44945" class="Symbol">((</a><a id="44947" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="44949" class="Symbol">_</a> <a id="44951" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="44954" href="Category.Ambient.html#2115" class="Function">idC</a><a id="44957" class="Symbol">)</a> <a id="44959" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44961" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="44975" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="44977" class="Symbol">(</a><a id="44978" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="44982" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="44984" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="44985" class="Symbol">))</a><a id="44987" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="45002" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="45005" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="45009" class="Symbol">(</a><a id="45010" href="Monad.Instance.K.Strong.html#5557" class="Function">τ-comm</a> <a id="45017" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="45018" class="Symbol">)</a> <a id="45020" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
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<a id="45036" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="45038" class="Symbol">(</a><a id="45039" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a> <a id="45041" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="45043" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="45044" class="Symbol">)</a> <a id="45046" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45048" class="Symbol">(</a><a id="45049" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45053" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45055" class="Symbol">(</a><a id="45056" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="45058" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="45059" class="Symbol">))</a> <a id="45093" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="45109" class="Keyword">where</a>
|
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<a id="45131" href="Monad.Instance.K.Commutative.html#45131" class="Function">by-uni</a> <a id="45138" class="Symbol">:</a> <a id="45140" class="Symbol">((</a><a id="45142" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="45144" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="45147" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45150" class="Symbol">)</a> <a id="45152" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45154" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="45168" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45170" class="Symbol">(</a><a id="45171" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45175" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45177" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="45178" class="Symbol">))</a> <a id="45181" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45183" class="Symbol">(</a><a id="45184" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="45186" class="Symbol">_</a> <a id="45188" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45190" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45193" class="Symbol">)</a> <a id="45195" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="45197" class="Symbol">(</a><a id="45198" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45202" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="45205" class="Symbol">(</a><a id="45206" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="45208" class="Symbol">_</a> <a id="45210" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45212" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45215" class="Symbol">))</a> <a id="45218" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45220" class="Symbol">(</a><a id="45221" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="45223" class="Symbol">_</a> <a id="45225" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="45228" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45231" class="Symbol">)</a> <a id="45233" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45235" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="45249" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45251" class="Symbol">(</a><a id="45252" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45256" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45258" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="45259" class="Symbol">)</a>
|
|||
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<a id="45277" href="Monad.Instance.K.Commutative.html#45131" class="Function">by-uni</a> <a id="45284" class="Symbol">=</a> <a id="45286" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
|||
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<a id="45310" class="Symbol">((</a><a id="45312" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="45314" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="45317" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45320" class="Symbol">)</a> <a id="45322" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45324" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="45338" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45340" class="Symbol">(</a><a id="45341" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45345" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45347" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="45348" class="Symbol">))</a> <a id="45351" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45353" class="Symbol">(</a><a id="45354" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="45356" class="Symbol">_</a> <a id="45358" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45360" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45363" class="Symbol">)</a> <a id="45379" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="45382" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="45388" class="Symbol">(</a><a id="45389" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="45395" class="Symbol">(</a><a id="45396" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="45400" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="45402" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="45410" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a> <a id="45422" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a> <a id="45430" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="45432" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="45436" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a><a id="45439" class="Symbol">))</a> <a id="45442" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="45462" class="Symbol">(</a><a id="45463" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="45465" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="45468" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45471" class="Symbol">)</a> <a id="45473" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45475" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="45489" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45491" class="Symbol">(</a><a id="45492" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="45494" class="Symbol">_</a> <a id="45496" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45498" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45501" class="Symbol">)</a> <a id="45503" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45505" class="Symbol">(</a><a id="45506" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45510" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45512" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="45513" class="Symbol">)</a> <a id="45531" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="45534" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="45542" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="45548" class="Symbol">(</a><a id="45549" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="45553" class="Symbol">(</a><a id="45554" href="Categories.Category.Distributive.Properties.html#3231" class="Function">distributeˡ⁻¹-natural</a> <a id="45576" class="Symbol">_</a> <a id="45578" class="Symbol">_</a> <a id="45580" class="Symbol">_</a> <a id="45582" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="45584" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="45592" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="45600" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="45605" class="Symbol">(</a><a id="45606" href="Category.Ambient.html#2218" class="Function">[]-unique</a> <a id="45616" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a> <a id="45628" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a><a id="45639" class="Symbol">)))</a> <a id="45643" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="45663" class="Symbol">(</a><a id="45664" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="45666" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="45669" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45672" class="Symbol">)</a> <a id="45674" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45676" class="Symbol">((</a><a id="45678" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="45680" class="Symbol">_</a> <a id="45682" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45684" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45688" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="45691" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="45693" class="Symbol">_</a> <a id="45695" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45697" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45700" class="Symbol">)</a> <a id="45702" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45704" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="45717" class="Symbol">)</a> <a id="45719" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45721" class="Symbol">(</a><a id="45722" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45726" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45728" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="45729" class="Symbol">)</a> <a id="45732" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="45735" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="45741" class="Symbol">(</a><a id="45742" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="45748" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a><a id="45753" class="Symbol">)</a> <a id="45755" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="45775" class="Symbol">((</a><a id="45777" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="45779" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45781" class="Symbol">(</a><a id="45782" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="45784" class="Symbol">_</a> <a id="45786" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45788" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45791" class="Symbol">)</a> <a id="45793" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="45796" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45800" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45802" class="Symbol">(</a><a id="45803" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="45805" class="Symbol">_</a> <a id="45807" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45809" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45812" class="Symbol">))</a> <a id="45815" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45817" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="45830" class="Symbol">)</a> <a id="45832" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45834" class="Symbol">(</a><a id="45835" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45839" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45841" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="45842" class="Symbol">)</a> <a id="45844" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="45847" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="45853" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="45855" class="Symbol">(</a><a id="45856" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="45865" class="Symbol">(</a><a id="45866" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="45872" href="Monad.Instance.K.Commutative.html#3084" class="Function">σ-η</a><a id="45875" class="Symbol">)</a> <a id="45877" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="45886" class="Symbol">)</a> <a id="45888" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="45896" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="45916" class="Symbol">(</a><a id="45917" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="45924" class="Symbol">(</a><a id="45925" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="45927" class="Symbol">_)</a> <a id="45930" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45932" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="45934" class="Symbol">_</a> <a id="45936" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="45939" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="45941" class="Symbol">_</a> <a id="45943" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45945" href="Category.Ambient.html#2115" class="Function">idC</a><a id="45948" class="Symbol">)</a> <a id="45950" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45952" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="45966" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="45968" class="Symbol">(</a><a id="45969" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="45973" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="45975" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="45976" class="Symbol">)</a> <a id="45985" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="45988" class="Symbol">(</a><a id="45989" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="45998" href="Categories.Monad.Relative.html#953" class="Function">kleisliK.identityʳ</a> <a id="46017" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="46021" class="Symbol">)</a> <a id="46023" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="46031" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="46051" class="Symbol">(</a><a id="46052" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="46054" class="Symbol">_</a> <a id="46056" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="46059" class="Symbol">(</a><a id="46060" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="46062" class="Symbol">_</a> <a id="46064" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46066" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46069" class="Symbol">))</a> <a id="46072" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46074" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="46088" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46090" class="Symbol">(</a><a id="46091" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="46095" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46097" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="46098" class="Symbol">)</a> <a id="46120" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="46123" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="46127" class="Symbol">(</a><a id="46128" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="46134" class="Symbol">(</a><a id="46135" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="46141" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="46143" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="46152" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="46162" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a><a id="46171" class="Symbol">))</a> <a id="46174" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="46194" class="Symbol">(</a><a id="46195" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="46199" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="46202" class="Symbol">(</a><a id="46203" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="46205" class="Symbol">_</a> <a id="46207" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46209" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46212" class="Symbol">))</a> <a id="46215" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46217" class="Symbol">(</a><a id="46218" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="46220" class="Symbol">_</a> <a id="46222" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="46225" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46228" class="Symbol">)</a> <a id="46230" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46232" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="46246" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46248" class="Symbol">(</a><a id="46249" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="46253" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46255" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="46256" class="Symbol">)</a> <a id="46263" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="46277" href="Monad.Instance.K.Commutative.html#46277" class="Function">comm₇</a> <a id="46283" class="Symbol">:</a> <a id="46285" class="Symbol">∀</a> <a id="46287" class="Symbol">{</a><a id="46288" href="Monad.Instance.K.Commutative.html#46288" class="Bound">U</a><a id="46289" class="Symbol">}</a> <a id="46291" class="Symbol">(</a><a id="46292" href="Monad.Instance.K.Commutative.html#46292" class="Bound">g</a> <a id="46294" class="Symbol">:</a> <a id="46296" href="Monad.Instance.K.Commutative.html#46288" class="Bound">U</a> <a id="46298" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="46300" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="46304" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a> <a id="46306" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="46308" href="Monad.Instance.K.Commutative.html#46288" class="Bound">U</a><a id="46309" class="Symbol">)</a> <a id="46311" class="Symbol">→</a> <a id="46313" class="Symbol">(</a><a id="46314" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="46316" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46318" class="Symbol">(</a><a id="46319" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="46323" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46325" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="46327" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="46328" class="Symbol">))</a> <a id="46331" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46333" class="Symbol">(</a><a id="46334" href="Monad.Instance.K.Commutative.html#46292" class="Bound">g</a> <a id="46336" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="46338" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46340" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46343" class="Symbol">)</a> <a id="46345" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="46347" class="Symbol">((</a><a id="46349" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="46351" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46353" class="Symbol">(</a><a id="46354" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="46358" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46360" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="46362" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="46363" class="Symbol">)</a> <a id="46365" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="46368" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46371" class="Symbol">)</a> <a id="46373" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46375" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="46389" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46391" class="Symbol">(</a><a id="46392" href="Monad.Instance.K.Commutative.html#46292" class="Bound">g</a> <a id="46394" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46396" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46399" class="Symbol">))</a> <a id="46402" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a>
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<a id="46416" href="Monad.Instance.K.Commutative.html#46277" class="Function">comm₇</a> <a id="46422" class="Symbol">{</a><a id="46423" href="Monad.Instance.K.Commutative.html#46423" class="Bound">U</a><a id="46424" class="Symbol">}</a> <a id="46426" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="46428" class="Symbol">=</a> <a id="46430" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="46604" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="46606" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46608" class="Symbol">(</a><a id="46609" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="46611" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="46613" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46615" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46618" class="Symbol">)</a> <a id="46620" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46622" class="Symbol">(</a><a id="46623" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="46627" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46629" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="46631" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="46632" class="Symbol">)</a> <a id="46687" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="46690" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="46696" class="Symbol">(</a><a id="46697" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="46703" class="Symbol">(</a><a id="46704" href="Monad.Instance.K.Commutative.html#3465" class="Function">σ-comm</a> <a id="46711" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a><a id="46712" class="Symbol">))</a> <a id="46715" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="46731" class="Symbol">(</a><a id="46732" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="46739" class="Symbol">(</a><a id="46740" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="46742" class="Symbol">_)</a> <a id="46745" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46747" class="Symbol">((</a><a id="46749" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="46751" class="Symbol">_</a> <a id="46753" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="46756" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46759" class="Symbol">)</a> <a id="46761" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46763" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="46777" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46779" class="Symbol">(</a><a id="46780" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="46782" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46784" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46787" class="Symbol">))</a> <a id="46790" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="46791" class="Symbol">)</a> <a id="46793" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46795" class="Symbol">(</a><a id="46796" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="46800" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46802" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="46804" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="46805" class="Symbol">)</a> <a id="46814" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="46817" href="Monad.Instance.K.Commutative.html#8711" class="Function">extend-preserve</a> <a id="46833" class="Symbol">(</a><a id="46834" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="46836" class="Symbol">(</a><a id="46837" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a> <a id="46839" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="46841" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="46842" class="Symbol">))</a> <a id="46845" class="Symbol">_</a> <a id="46847" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="46855" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="46871" class="Symbol">((</a><a id="46873" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="46880" class="Symbol">(</a><a id="46881" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="46883" class="Symbol">_)</a> <a id="46886" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="46889" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46892" class="Symbol">)</a> <a id="46894" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46896" class="Symbol">(</a><a id="46897" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="46899" class="Symbol">_</a> <a id="46901" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="46904" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46907" class="Symbol">)</a> <a id="46909" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46911" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="46925" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46927" class="Symbol">(</a><a id="46928" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="46930" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46932" href="Category.Ambient.html#2115" class="Function">idC</a><a id="46935" class="Symbol">))</a> <a id="46938" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="46940" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="46942" class="Symbol">(</a><a id="46943" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="46947" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="46949" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="46951" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="46952" class="Symbol">)</a> <a id="46954" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="46957" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="46961" class="Symbol">(</a><a id="46962" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a> <a id="46975" class="Symbol">(</a><a id="46976" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="46985" class="Symbol">_)</a> <a id="46988" class="Symbol">(</a><a id="46989" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="46993" href="Monad.Instance.K.Commutative.html#47139" class="Function">by-uni</a><a id="46999" class="Symbol">))</a> <a id="47002" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="47018" class="Symbol">((</a><a id="47020" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="47022" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47024" class="Symbol">(</a><a id="47025" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47029" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47031" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="47033" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="47034" class="Symbol">)</a> <a id="47036" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47039" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47042" class="Symbol">)</a> <a id="47044" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47046" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="47060" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47062" class="Symbol">(</a><a id="47063" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="47065" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47067" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47070" class="Symbol">))</a><a id="47072" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="47101" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="47117" class="Keyword">where</a>
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<a id="47139" href="Monad.Instance.K.Commutative.html#47139" class="Function">by-uni</a> <a id="47146" class="Symbol">:</a> <a id="47148" class="Symbol">((</a><a id="47150" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="47157" class="Symbol">(</a><a id="47158" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="47160" class="Symbol">_)</a> <a id="47163" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47166" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47169" class="Symbol">)</a> <a id="47171" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47173" class="Symbol">(</a><a id="47174" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="47176" class="Symbol">_</a> <a id="47178" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47181" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47184" class="Symbol">)</a> <a id="47186" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47188" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="47202" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47204" class="Symbol">(</a><a id="47205" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="47207" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47209" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47212" class="Symbol">))</a> <a id="47215" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47217" class="Symbol">(</a><a id="47218" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47222" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47224" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="47226" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="47227" class="Symbol">)</a> <a id="47229" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="47231" class="Symbol">(</a><a id="47232" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47236" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47239" class="Symbol">(</a><a id="47240" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47244" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47246" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="47248" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="47249" class="Symbol">))</a> <a id="47252" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47254" class="Symbol">((</a><a id="47256" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="47258" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47260" class="Symbol">(</a><a id="47261" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47265" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47267" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="47269" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="47270" class="Symbol">))</a> <a id="47273" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47276" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47279" class="Symbol">)</a> <a id="47281" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47283" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="47297" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47299" class=
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<a id="47325" href="Monad.Instance.K.Commutative.html#47139" class="Function">by-uni</a> <a id="47332" class="Symbol">=</a> <a id="47334" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="47358" class="Symbol">((</a><a id="47360" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="47367" class="Symbol">(</a><a id="47368" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="47370" class="Symbol">_)</a> <a id="47373" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47376" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47379" class="Symbol">)</a> <a id="47381" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47383" class="Symbol">(</a><a id="47384" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="47386" class="Symbol">_</a> <a id="47388" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47391" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47394" class="Symbol">)</a> <a id="47396" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47398" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="47412" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47414" class="Symbol">(</a><a id="47415" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="47417" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47419" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47422" class="Symbol">))</a> <a id="47425" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47427" class="Symbol">(</a><a id="47428" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47432" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47434" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="47436" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="47437" class="Symbol">)</a> <a id="47452" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="47455" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="47461" class="Symbol">(</a><a id="47462" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="47468" class="Symbol">(</a><a id="47469" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="47475" class="Symbol">(</a><a id="47476" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="47480" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="47482" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="47490" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a> <a id="47498" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a> <a id="47510" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="47512" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="47516" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a><a id="47519" class="Symbol">)))</a> <a id="47523" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="47543" class="Symbol">(</a><a id="47544" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="47551" class="Symbol">(</a><a id="47552" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="47554" class="Symbol">_)</a> <a id="47557" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47560" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47563" class="Symbol">)</a> <a id="47565" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47567" class="Symbol">(</a><a id="47568" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="47570" class="Symbol">_</a> <a id="47572" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47575" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47578" class="Symbol">)</a> <a id="47580" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47582" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="47596" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47598" class="Symbol">(</a><a id="47599" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47603" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47605" class="Symbol">(</a><a id="47606" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="47608" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="47609" class="Symbol">))</a> <a id="47612" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47614" class="Symbol">(</a><a id="47615" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="47617" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47619" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47622" class="Symbol">)</a> <a id="47637" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="47640" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="47648" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="47656" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="47662" class="Symbol">(</a><a id="47663" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="47667" class="Symbol">(</a><a id="47668" href="Categories.Category.Distributive.Properties.html#4502" class="Function">distributeʳ⁻¹-natural</a> <a id="47690" class="Symbol">_</a> <a id="47692" class="Symbol">_</a> <a id="47694" class="Symbol">_</a> <a id="47696" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="47698" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="47706" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="47714" class="Symbol">(</a><a id="47715" href="Category.Ambient.html#2218" class="Function">[]-unique</a> <a id="47725" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a> <a id="47737" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a><a id="47748" class="Symbol">)</a> <a id="47750" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="47754" class="Symbol">))</a> <a id="47757" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="47777" class="Symbol">(</a><a id="47778" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="47785" class="Symbol">(</a><a id="47786" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="47788" class="Symbol">_)</a> <a id="47791" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47794" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47797" class="Symbol">)</a> <a id="47799" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47801" class="Symbol">(</a><a id="47802" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="47804" class="Symbol">_</a> <a id="47806" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47809" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47812" class="Symbol">)</a> <a id="47814" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47816" class="Symbol">((</a><a id="47818" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47822" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47824" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="47826" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="47828" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47831" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47835" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47837" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="47839" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="47840" class="Symbol">)</a> <a id="47842" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47844" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a><a id="47857" class="Symbol">)</a> <a id="47859" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47861" class="Symbol">(</a><a id="47862" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="47864" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47866" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47869" class="Symbol">)</a> <a id="47871" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="47874" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="47880" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="47886" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="47888" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="47894" class="Symbol">(</a><a id="47895" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="47901" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a><a id="47906" class="Symbol">)</a> <a id="47908" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="47928" class="Symbol">((</a><a id="47930" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="47932" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47934" class="Symbol">(</a><a id="47935" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47939" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47941" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="47943" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="47944" class="Symbol">)</a> <a id="47946" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="47949" class="Symbol">(</a><a id="47950" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47954" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47956" href="Category.Ambient.html#2115" class="Function">idC</a><a id="47959" class="Symbol">)</a> <a id="47961" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47963" class="Symbol">(</a><a id="47964" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="47968" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="47970" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="47972" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="47973" class="Symbol">))</a> <a id="47976" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47978" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a><a id="47991" class="Symbol">)</a> <a id="47993" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="47995" class="Symbol">(</a><a id="47996" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="47998" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48000" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48003" class="Symbol">)</a> <a id="48022" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="48025" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="48031" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="48033" class="Symbol">(</a><a id="48034" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="48043" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="48048" class="Symbol">(</a><a id="48049" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="48055" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="48064" class="Symbol">))</a> <a id="48067" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="48075" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="48095" class="Symbol">(</a><a id="48096" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="48098" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48100" class="Symbol">(</a><a id="48101" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="48105" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48107" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="48109" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="48110" class="Symbol">)</a> <a id="48112" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48115" class="Symbol">(</a><a id="48116" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="48120" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48122" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="48124" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="48125" class="Symbol">))</a> <a id="48128" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48130" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="48144" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48146" class="Symbol">(</a><a id="48147" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="48149" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48151" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48154" class="Symbol">)</a> <a id="48189" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="48193" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="48199" class="Symbol">(</a><a id="48200" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="48206" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="48208" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="48217" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="48227" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a><a id="48236" class="Symbol">)</a> <a id="48238" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="48258" class="Symbol">(</a><a id="48259" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="48263" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48266" class="Symbol">(</a><a id="48267" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="48271" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48273" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="48275" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="48276" class="Symbol">))</a> <a id="48279" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48281" class="Symbol">((</a><a id="48283" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="48285" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48287" class="Symbol">(</a><a id="48288" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="48292" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48294" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a> <a id="48296" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="48297" class="Symbol">))</a> <a id="48300" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48303" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48306" class="Symbol">)</a> <a id="48308" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48310" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="48324" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48326" class="Symbol">(</a><a id="48327" href="Monad.Instance.K.Commutative.html#46426" class="Bound">g</a> <a id="48329" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48331" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48334" class="Symbol">)</a> <a id="48352" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="48366" href="Monad.Instance.K.Commutative.html#48366" class="Function">comm₈</a> <a id="48372" class="Symbol">:</a> <a id="48374" class="Symbol">∀</a> <a id="48376" class="Symbol">{</a><a id="48377" href="Monad.Instance.K.Commutative.html#48377" class="Bound">U</a><a id="48378" class="Symbol">}</a> <a id="48380" class="Symbol">(</a><a id="48381" href="Monad.Instance.K.Commutative.html#48381" class="Bound">g</a> <a id="48383" class="Symbol">:</a> <a id="48385" href="Monad.Instance.K.Commutative.html#48377" class="Bound">U</a> <a id="48387" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="48389" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="48393" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a> <a id="48395" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="48397" href="Monad.Instance.K.Commutative.html#48377" class="Bound">U</a><a id="48398" class="Symbol">)</a> <a id="48400" class="Symbol">→</a> <a id="48402" class="Symbol">((</a><a id="48404" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="48406" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48409" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48412" class="Symbol">)</a> <a id="48414" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48416" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="48430" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48432" class="Symbol">(</a><a id="48433" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="48437" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48439" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="48440" class="Symbol">))</a> <a id="48443" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="48445" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48447" class="Symbol">(</a><a id="48448" href="Monad.Instance.K.Commutative.html#48381" class="Bound">g</a> <a id="48450" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="48452" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48454" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48457" class="Symbol">)</a> <a id="48459" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="48461" class="Symbol">((((</a><a id="48465" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="48467" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48470" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48473" class="Symbol">)</a> <a id="48475" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48477" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="48491" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48493" class="Symbol">(</a><a id="48494" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="48498" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48500" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="48501" class="Symbol">))</a><a id="48503" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="48505" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48508" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48511" class="Symbol">)</a> <a id="48513" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48515" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="4852
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<a id="48555" href="Monad.Instance.K.Commutative.html#48366" class="Function">comm₈</a> <a id="48561" class="Symbol">{</a><a id="48562" href="Monad.Instance.K.Commutative.html#48562" class="Bound">U</a><a id="48563" class="Symbol">}</a> <a id="48565" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="48567" class="Symbol">=</a> <a id="48569" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="48589" class="Symbol">((</a><a id="48591" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="48593" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48596" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48599" class="Symbol">)</a> <a id="48601" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48603" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="48617" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48619" class="Symbol">(</a><a id="48620" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="48624" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48626" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="48627" class="Symbol">))</a><a id="48629" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="48631" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48633" class="Symbol">(</a><a id="48634" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="48636" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="48638" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48640" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48643" class="Symbol">)</a> <a id="48645" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="48648" href="Monad.Instance.K.Commutative.html#53171" class="Function">στ</a> <a id="48651" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="48667" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="48674" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="48676" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48678" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="48685" class="Symbol">(</a><a id="48686" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="48688" class="Symbol">_)</a> <a id="48691" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48693" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="48695" class="Symbol">_</a> <a id="48697" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48699" class="Symbol">(((</a><a id="48702" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="48704" class="Symbol">_</a> <a id="48706" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48709" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48712" class="Symbol">)</a> <a id="48714" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48716" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="48717" class="Symbol">)</a> <a id="48719" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="48721" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48723" class="Symbol">((</a><a id="48725" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="48727" class="Symbol">_</a> <a id="48729" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48732" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48735" class="Symbol">)</a> <a id="48737" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48739" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="48740" class="Symbol">)</a> <a id="48742" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="48743" class="Symbol">)</a> <a id="48749" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="48752" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="48760" class="Symbol">(</a><a id="48761" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="48765" class="Symbol">(</a><a id="48766" href="Monad.Instance.K.Commutative.html#9276" class="Function">comm-helper</a> <a id="48778" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="48780" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="48781" class="Symbol">))</a> <a id="48784" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="48800" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="48807" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="48809" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48811" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="48818" class="Symbol">(</a><a id="48819" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="48821" class="Symbol">_)</a> <a id="48824" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48826" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="48828" class="Symbol">_</a> <a id="48830" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48832" class="Symbol">(((</a><a id="48835" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="48837" class="Symbol">_</a> <a id="48839" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48842" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48845" class="Symbol">)</a> <a id="48847" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48849" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="48850" class="Symbol">)</a> <a id="48852" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="48854" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48856" class="Symbol">((</a><a id="48858" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="48860" class="Symbol">_</a> <a id="48862" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48865" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48868" class="Symbol">)</a> <a id="48870" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48872" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="48873" class="Symbol">)</a> <a id="48875" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="48876" class="Symbol">)</a> <a id="48882" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="48885" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="48889" href="Monad.Instance.K.Commutative.html#49028" class="Function">τσ</a> <a id="48892" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="48908" class="Symbol">((((</a><a id="48912" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="48914" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48917" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48920" class="Symbol">)</a> <a id="48922" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48924" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="48938" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48940" class="Symbol">(</a><a id="48941" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="48945" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48947" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="48948" class="Symbol">))</a><a id="48950" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="48952" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="48955" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48958" class="Symbol">)</a> <a id="48960" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48962" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="48976" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="48978" class="Symbol">(</a><a id="48979" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="48981" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="48983" href="Category.Ambient.html#2115" class="Function">idC</a><a id="48986" class="Symbol">))</a><a id="48988" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="48990" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="49006" class="Keyword">where</a>
|
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<a id="49028" href="Monad.Instance.K.Commutative.html#49028" class="Function">τσ</a> <a id="49031" class="Symbol">:</a> <a id="49033" class="Symbol">((((</a><a id="49037" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="49039" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49042" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49045" class="Symbol">)</a> <a id="49047" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49049" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="49063" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49065" class="Symbol">(</a><a id="49066" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="49070" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49072" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="49073" class="Symbol">))</a><a id="49075" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="49077" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49080" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49083" class="Symbol">)</a> <a id="49085" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49087" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="49101" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49103" class="Symbol">(</a><a id="49104" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="49106" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49108" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49111" class="Symbol">))</a><a id="49113" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="49115" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="49117" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="49124" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="49126" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49128" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="49135" class="Symbol">(</a><a id="49136" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="49138" class="Symbol">_)</a> <a id="49141" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49143" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="49145" class="Symbol">_</a> <a id="49147" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49149" class="Symbol">(((</a><a id="49152" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="49154" class="Symbol">_</a> <a id="49156" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49159" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49162" class="Symbol">)</a> <a id="49164" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49166" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="49167" class="Symbol">)</a> <a id="49169" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="49171" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49173" class="Symbol">((</a><a id="49175" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="49177" class="Symbol">_</a> <a id="49179" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49182" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49185" class="Symbol">)</a> <a id="49187" href="Categories.Category.Cor
|
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<a id="49211" href="Monad.Instance.K.Commutative.html#49028" class="Function">τσ</a> <a id="49214" class="Symbol">=</a> <a id="49216" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
|||
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<a id="49241" class="Symbol">(((((</a><a id="49246" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="49248" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49251" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49254" class="Symbol">)</a> <a id="49256" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49258" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="49272" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49274" class="Symbol">(</a><a id="49275" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="49279" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49281" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="49282" class="Symbol">))</a><a id="49284" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="49286" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49289" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49292" class="Symbol">)</a> <a id="49294" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49296" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="49310" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49312" class="Symbol">(</a><a id="49313" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="49315" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49317" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49320" class="Symbol">))</a><a id="49322" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="49323" class="Symbol">)</a> <a id="49365" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="49369" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="49378" class="Symbol">(</a><a id="49379" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="49388" class="Symbol">_)</a> <a id="49391" class="Symbol">(</a><a id="49392" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="49398" class="Symbol">(</a><a id="49399" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="49405" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="49407" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="49416" href="Categories.Monad.Relative.html#953" class="Function">kleisliK.identityʳ</a> <a id="49435" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="49444" class="Symbol">))</a> <a id="49447" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
|
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<a id="49468" class="Symbol">((</a><a id="49470" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="49477" class="Symbol">(((</a><a id="49480" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="49482" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49485" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49488" class="Symbol">)</a> <a id="49490" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49492" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="49506" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49508" class="Symbol">(</a><a id="49509" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="49513" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49515" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="49516" class="Symbol">))</a> <a id="49519" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="49520" class="Symbol">)</a> <a id="49522" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49525" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49528" class="Symbol">)</a> <a id="49530" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49532" class="Symbol">(</a><a id="49533" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="49535" class="Symbol">_</a> <a id="49537" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49540" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49543" class="Symbol">)</a> <a id="49545" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49547" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="49561" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49563" class="Symbol">(</a><a id="49564" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="49566" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49568" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49571" class="Symbol">))</a> <a id="49574" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="49592" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="49596" href="Monad.Instance.K.Commutative.html#8711" class="Function">extend-preserve</a> <a id="49612" class="Symbol">(((</a><a id="49615" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="49617" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49620" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49623" class="Symbol">)</a> <a id="49625" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49627" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="49641" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49643" class="Symbol">(</a><a id="49644" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="49648" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49650" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="49651" class="Symbol">))</a> <a id="49654" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="49655" class="Symbol">)</a> <a id="49657" class="Symbol">((</a><a id="49659" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="49661" class="Symbol">_</a> <a id="49663" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49666" href="Category.Ambient.ht
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<a id="49721" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="49728" class="Symbol">(((</a><a id="49731" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="49733" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49736" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49739" class="Symbol">)</a> <a id="49741" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49743" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="49757" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49759" class="Symbol">(</a><a id="49760" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="49764" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49766" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="49767" class="Symbol">))</a> <a id="49770" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="49771" class="Symbol">)</a> <a id="49773" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49775" class="Symbol">((</a><a id="49777" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="49779" class="Symbol">_</a> <a id="49781" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49784" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49787" class="Symbol">)</a> <a id="49789" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49791" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="49805" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49807" class="Symbol">(</a><a id="49808" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="49810" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49812" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49815" class="Symbol">))</a> <a id="49818" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="49845" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="49848" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="49856" class="Symbol">(</a><a id="49857" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="49866" class="Symbol">(</a><a id="49867" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="49876" class="Symbol">_)</a> <a id="49879" class="Symbol">((</a><a id="49881" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="49890" class="Symbol">(</a><a id="49891" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="49895" href="Monad.Instance.K.Commutative.html#3084" class="Function">σ-η</a><a id="49898" class="Symbol">)</a> <a id="49900" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="49904" class="Symbol">)</a> <a id="49906" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="49913" class="Symbol">))</a> <a id="49916" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="49937" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="49944" class="Symbol">(((</a><a id="49947" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="49949" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="49952" href="Category.Ambient.html#2115" class="Function">idC</a><a id="49955" class="Symbol">)</a> <a id="49957" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49959" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="49973" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49975" class="Symbol">(</a><a id="49976" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="49980" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="49982" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="49983" class="Symbol">))</a> <a id="49986" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="49987" class="Symbol">)</a> <a id="49989" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49991" class="Symbol">((</a><a id="49993" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="49995" class="Symbol">_</a> <a id="49997" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="49999" class="Symbol">(</a><a id="50000" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="50002" class="Symbol">_</a> <a id="50004" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="50006" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50009" class="Symbol">)</a> <a id="50011" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="50014" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50017" class="Symbol">)</a> <a id="50019" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50021" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="50035" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50037" class="Symbol">(</a><a id="50038" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="50040" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="50042" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50045" class="Symbol">))</a> <a id="50048" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="50061" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="50065" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="50073" class="Symbol">(</a><a id="50074" href="Monad.Instance.K.Commutative.html#3465" class="Function">σ-comm</a> <a id="50081" class="Symbol">_</a> <a id="50083" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="50085" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="50094" class="Symbol">(</a><a id="50095" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="50104" class="Symbol">_)</a> <a id="50107" href="Monad.Instance.K.Commutative.html#52419" class="Function">comm</a><a id="50111" class="Symbol">)</a> <a id="50113" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="50134" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="50141" class="Symbol">(((</a><a id="50144" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="50146" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="50149" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50152" class="Symbol">)</a> <a id="50154" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50156" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="50170" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50172" class="Symbol">(</a><a id="50173" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="50177" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="50179" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="50180" class="Symbol">))</a> <a id="50183" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="50184" class="Symbol">)</a> <a id="50186" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50188" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="50190" class="Symbol">_</a> <a id="50192" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50194" class="Symbol">(((</a><a id="50197" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="50199" class="Symbol">_</a> <a id="50201" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="50204" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50207" class="Symbol">)</a> <a id="50209" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50211" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="50212" class="Symbol">)</a><a id="50213" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="50215" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="50217" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50220" class="Symbol">)</a> <a id="50258" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="50262" class="Symbol">(</a><a id="50263" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="50281" class="Symbol">(</a><a id="50282" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="50291" class="Symbol">(</a><a id="50292" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="50301" class="Symbol">_)</a> <a id="50304" class="Symbol">(</a><a id="50305" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="50311" class="Symbol">(</a><a id="50312" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="50318" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="50320" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="50329" href="Categories.Monad.Relative.html#953" class="Function">kleisliK.identityʳ</a> <a id="50348" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="50357" class="Symbol">))))</a> <a id="50362" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="50370" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="50391" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="50398" class="Symbol">((((</a><a id="50402" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="50409" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="50411" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="50414" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50417" class="Symbol">)</a> <a id="50419" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50421" class="Symbol">(</a><a id="50422" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="50424" class="Symbol">_</a> <a id="50426" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="50429" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50432" class="Symbol">)</a> <a id="50434" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50436" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="50450" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50452" class="Symbol">(</a><a id="50453" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="50457" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="50459" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="50460" class="Symbol">))</a><a id="50462" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="50463" class="Symbol">))</a> <a id="50466" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50468" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="50470" class="Symbol">_</a> <a id="50472" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50474" class="Symbol">(((</a><a id="50477" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="50479" class="Symbol">_</a> <a id="50481" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="50484" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50487" class="Symbol">)</a> <a id="50489" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50491" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="50492" class="Symbol">)</a><a id="50493" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="50495" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="50497" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50500" class="Symbol">)</a> <a id="50515" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="50519" class="Symbol">(</a><a id="50520" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="50538" class="Symbol">(</a><a id="50539" href="Monad.Instance.K.Commutative.html#8711" class="Function">extend-preserve</a> <a id="50555" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="50557" class="Symbol">_))</a> <a id="50561" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="50569" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="50590" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="50597" class="Symbol">(</a><a id="50598" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="50605" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="50607" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50609" class="Symbol">(((</a><a id="50612" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="50614" class="Symbol">_</a> <a id="50616" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="50619" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50622" class="Symbol">)</a> <a id="50624" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50626" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="50640" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50642" class="Symbol">(</a><a id="50643" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="50647" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="50649" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="50650" class="Symbol">))</a><a id="50652" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="50653" class="Symbol">))</a> <a id="50656" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50658" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="50660" class="Symbol">_</a> <a id="50662" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50664" class="Symbol">(((</a><a id="50667" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="50669" class="Symbol">_</a> <a id="50671" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="50674" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50677" class="Symbol">)</a> <a id="50679" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50681" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="50682" class="Symbol">)</a><a id="50683" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="50685" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="50687" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50690" class="Symbol">)</a> <a id="50714" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="50718" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="50724" href="Categories.Monad.Relative.html#1190" class="Function">kleisliK.sym-assoc</a> <a id="50743" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="50764" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="50771" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="50773" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50775" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="50782" class="Symbol">(((</a><a id="50785" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="50787" class="Symbol">_</a> <a id="50789" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="50792" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50795" class="Symbol">)</a> <a id="50797" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50799" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="50813" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50815" class="Symbol">(</a><a id="50816" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="50820" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="50822" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="50823" class="Symbol">))</a><a id="50825" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="50826" class="Symbol">)</a> <a id="50828" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50830" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="50832" class="Symbol">_</a> <a id="50834" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50836" class="Symbol">(((</a><a id="50839" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="50841" class="Symbol">_</a> <a id="50843" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="50846" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50849" class="Symbol">)</a> <a id="50851" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="50853" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="50854" class="Symbol">)</a><a id="50855" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="50857" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="50859" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50862" class="Symbol">)</a> <a id="50888" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="50892" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="50900" class="Symbol">((</a><a id="50902" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="50920" class="Symbol">(</a><a id="50921" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="50930" class="Symbol">(</a><a id="50931" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="50940" class="Symbol">_)</a> <a id="50943" class="Symbol">(</a><a id="50944" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="50952" class="Symbol">(</a><a id="50953" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="50959" class="Symbol">(</a><a id="50960" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="50964" class="Symbol">(</a><a id="50965" href="Categories.Category.Distributive.Properties.html#3231" class="Function">distributeˡ⁻¹-natural</a> <a id="50987" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="50991" class="Symbol">_</a> <a id="50993" href="Category.Ambient.html#2115" class="Function">idC</a><a id="50996" class="Symbol">))))</a> <a id="51001" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="51003" href="Algebra.Elgot.
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<a id="51144" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="51151" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="51153" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51155" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="51162" class="Symbol">(((</a><a id="51165" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="51167" class="Symbol">_</a> <a id="51169" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51172" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51175" class="Symbol">)</a> <a id="51177" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51179" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="51193" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51195" class="Symbol">(</a><a id="51196" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="51200" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="51202" class="Symbol">(</a><a id="51203" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="51205" class="Symbol">_</a> <a id="51207" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51210" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51213" class="Symbol">))</a> <a id="51216" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51218" class="Symbol">(</a><a id="51219" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="51223" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="51225" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="51226" class="Symbol">))</a> <a id="51229" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="51230" class="Symbol">)</a> <a id="51232" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51234" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="51236" class="Symbol">_</a> <a id="51238" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51240" class="Symbol">(((</a><a id="51243" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="51245" class="Symbol">_</a> <a id="51247" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51250" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51253" class="Symbol">)</a> <a id="51255" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51257" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="51258" class="Symbol">)</a><a id="51259" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="51261" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="51263" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51266" class="Symbol">)</a> <a id="51268" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="51271" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="51279" class="Symbol">(</a><a id="51280" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="51298" class="Symbol">(</a><a id="51299" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="51308" class="Symbol">(</a><a id="51309" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="51318" class="Symbol">_)</a> <a id="51321" class="Symbol">(</a><a id="51322" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="51330" class="Symbol">(</a><a id="51331" href="Categories.Category.Core.html#2734" class="Function Operator">ref
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<a id="51403" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="51410" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="51412" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51414" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="51421" class="Symbol">(((</a><a id="51424" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="51426" class="Symbol">_</a> <a id="51428" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51431" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51434" class="Symbol">)</a> <a id="51436" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51438" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="51452" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51454" class="Symbol">(</a><a id="51455" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="51459" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="51461" class="Symbol">(</a><a id="51462" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="51464" class="Symbol">_</a> <a id="51466" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51469" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51472" class="Symbol">)</a> <a id="51474" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51476" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="51477" class="Symbol">))</a> <a id="51480" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="51481" class="Symbol">)</a> <a id="51483" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51485" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="51487" class="Symbol">_</a> <a id="51489" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51491" class="Symbol">(((</a><a id="51494" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="51496" class="Symbol">_</a> <a id="51498" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51501" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51504" class="Symbol">)</a> <a id="51506" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51508" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="51509" class="Symbol">)</a><a id="51510" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="51512" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="51514" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51517" class="Symbol">)</a> <a id="51527" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="51531" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="51539" class="Symbol">((</a><a id="51541" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="51559" class="Symbol">(</a><a id="51560" href="Monad.Instance.K.Strong.html#5557" class="Function">τ-comm</a> <a id="51567" class="Symbol">_))</a> <a id="51571" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="51578" class="Symbol">)</a> <a id="51580" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="51601" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="51608" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="51610" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51612" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="51619" class="Symbol">(</a><a id="51620" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="51622" class="Symbol">_</a> <a id="51624" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51626" class="Symbol">(</a><a id="51627" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="51631" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="51633" class="Symbol">((</a><a id="51635" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="51637" class="Symbol">_</a> <a id="51639" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51642" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51645" class="Symbol">)</a> <a id="51647" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51649" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="51650" class="Symbol">)</a> <a id="51652" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="51653" class="Symbol">))</a> <a id="51656" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51658" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="51660" class="Symbol">_</a> <a id="51662" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51664" class="Symbol">(((</a><a id="51667" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="51669" class="Symbol">_</a> <a id="51671" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51674" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51677" class="Symbol">)</a> <a id="51679" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51681" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="51682" class="Symbol">)</a><a id="51683" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="51685" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="51687" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51690" class="Symbol">)</a> <a id="51725" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="51729" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="51737" class="Symbol">(</a><a id="51738" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="51744" class="Symbol">(</a><a id="51745" href="Category.Ambient.html#10469" class="Function">extend∘F₁</a> <a id="51755" href="Monad.Instance.K.html#1609" class="Function">monadK</a> <a id="51762" class="Symbol">(</a><a id="51763" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="51765" class="Symbol">_)</a> <a id="51768" class="Symbol">_))</a> <a id="51772" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="51793" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="51800" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="51802" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51804" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="51811" class="Symbol">(</a><a id="51812" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="51814" class="Symbol">_)</a> <a id="51817" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51819" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="51823" class="Symbol">(</a><a id="51824" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="51828" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="51830" class="Symbol">((</a><a id="51832" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="51834" class="Symbol">_</a> <a id="51836" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51839" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51842" class="Symbol">)</a> <a id="51844" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51846" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="51847" class="Symbol">)</a> <a id="51849" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="51850" class="Symbol">)</a> <a id="51852" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51854" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="51856" class="Symbol">_</a> <a id="51858" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51860" class="Symbol">(((</a><a id="51863" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="51865" class="Symbol">_</a> <a id="51867" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51870" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51873" class="Symbol">)</a> <a id="51875" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="51877" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="51878" class="Symbol">)</a><a id="51879" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="51881" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="51883" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51886" class="Symbol">)</a> <a id="51917" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="51920" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="51928" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="51936" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="51942" class="Symbol">(</a><a id="51943" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="51947" class="Symbol">(</a><a id="51948" href="Monad.Instance.K.Commutative.html#5166" class="Function">σ-natural</a> <a id="51958" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="51962" class="Symbol">(((</a><a id="51965" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="51967" class="Symbol">(</a><a id="51968" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="51972" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="51973" class="Symbol">)</a> <a id="51975" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="51978" href="Category.Ambient.html#2115" class="Function">idC</a><a id="51981" class="Symbol">)</a> <a id="51983" href="Categories.Category.Core.html#656" class="Function Oper
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<a id="52014" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="52021" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="52023" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52025" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="52032" class="Symbol">(</a><a id="52033" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="52035" class="Symbol">_)</a> <a id="52038" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52040" class="Symbol">(</a><a id="52041" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="52043" class="Symbol">_</a> <a id="52045" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52047" class="Symbol">(</a><a id="52048" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="52052" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="52056" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52058" class="Symbol">((</a><a id="52060" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="52062" class="Symbol">_</a> <a id="52064" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52067" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52070" class="Symbol">)</a> <a id="52072" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52074" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="52075" class="Symbol">)</a> <a id="52077" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="52078" class="Symbol">))</a> <a id="52081" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52083" class="Symbol">(((</a><a id="52086" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="52088" class="Symbol">_</a> <a id="52090" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52093" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52096" class="Symbol">)</a> <a id="52098" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52100" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="52101" class="Symbol">)</a><a id="52102" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="52104" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52106" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52109" class="Symbol">)</a> <a id="52138" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="52141" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="52149" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="52157" class="Symbol">(</a><a id="52158" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="52164" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="52166" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="52174" class="Symbol">(</a><a id="52175" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="52179" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="52181" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="52190" class="Symbol">(</a><a id="52191" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="52197" href="Categories.Functor.Core.html#511" class="Function">monadK.F.identity</a><a id="52214" class="Symbol">)</a> <a id="52216" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a><a id="52225" class="Symbol">))</a> <a
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<a id="52249" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="52256" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="52258" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52260" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="52267" class="Symbol">(</a><a id="52268" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="52270" class="Symbol">_)</a> <a id="52273" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52275" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="52277" class="Symbol">_</a> <a id="52279" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52281" class="Symbol">(((</a><a id="52284" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="52286" class="Symbol">_</a> <a id="52288" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52291" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52294" class="Symbol">)</a> <a id="52296" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52298" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="52299" class="Symbol">)</a> <a id="52301" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="52303" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52305" class="Symbol">((</a><a id="52307" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="52309" class="Symbol">_</a> <a id="52311" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52314" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52317" class="Symbol">)</a> <a id="52319" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52321" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="52322" class="Symbol">)</a> <a id="52324" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="52325" class="Symbol">)</a> <a id="52373" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="52393" class="Keyword">where</a>
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<a id="52419" href="Monad.Instance.K.Commutative.html#52419" class="Function">comm</a> <a id="52424" class="Symbol">:</a> <a id="52426" class="Symbol">(</a><a id="52427" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="52429" class="Symbol">_</a> <a id="52431" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52434" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52437" class="Symbol">)</a> <a id="52439" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52441" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="52455" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52457" class="Symbol">(((</a><a id="52460" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="52462" class="Symbol">_</a> <a id="52464" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52467" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52470" class="Symbol">)</a> <a id="52472" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52474" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="52476" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52478" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52481" class="Symbol">))</a> <a id="52484" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="52486" class="Symbol">(</a><a id="52487" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="52489" class="Symbol">_</a> <a id="52491" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52493" class="Symbol">(</a><a id="52494" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="52496" class="Symbol">_</a> <a id="52498" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52500" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52503" class="Symbol">)</a> <a id="52505" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52508" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52511" class="Symbol">)</a> <a id="52513" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52515" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="52529" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52531" class="Symbol">(</a><a id="52532" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="52534" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52536" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52539" class="Symbol">)</a>
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<a id="52561" href="Monad.Instance.K.Commutative.html#52419" class="Function">comm</a> <a id="52566" class="Symbol">=</a> <a id="52568" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="52572" class="Symbol">(</a><a id="52573" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="52601" class="Symbol">(</a><a id="52602" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="52604" class="Symbol">_</a> <a id="52606" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52608" class="Symbol">(</a><a id="52609" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="52611" class="Symbol">_</a> <a id="52613" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52615" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52618" class="Symbol">)</a> <a id="52620" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52623" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52626" class="Symbol">)</a> <a id="52628" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52630" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="52644" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52646" class="Symbol">(</a><a id="52647" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="52649" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52651" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52654" class="Symbol">)</a> <a id="52667" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="52671" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="52677" class="Symbol">(</a><a id="52678" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="52684" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="52686" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="52695" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="52700" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="52709" class="Symbol">)</a> <a id="52711" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="52735" class="Symbol">(</a><a id="52736" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="52738" class="Symbol">_</a> <a id="52740" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52743" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52746" class="Symbol">)</a> <a id="52748" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52750" class="Symbol">((</a><a id="52752" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="52754" class="Symbol">_</a> <a id="52756" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52758" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52761" class="Symbol">)</a> <a id="52763" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52766" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52769" class="Symbol">)</a> <a id="52771" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52773" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="52787" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52789" class="Symbol">(</a><a id="52790" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="52792" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52794" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52797" class="Symbol">)</a> <a id="52801" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="52804" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="52812" class="Symbol">(</a><a id="52813" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="52819" class="Symbol">((</a><a id="52821" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="52830" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="52835" class="Symbol">(</a><a id="52836" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="52840" class="Symbol">(</a><a id="52841" href="Category.Ambient.html#2592" class="Function">⟨⟩-unique</a> <a id="52851" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a> <a id="52859" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a><a id="52866" class="Symbol">)))</a> <a id="52870" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="52878" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="52880" href="Categories.Category.Distributive.Properties.html#4502" class="Function">distributeʳ⁻¹-natural</a> <a id="52902" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="52906" class="Symbol">(</a><a id="52907" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="52909" class="Symbol">(</a><a id="52910" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="52914" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a><a id="52915" class="Symbol">))</a> <a id="52918" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52921" class="Symbol">))</a> <a id="52924" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="52948" class="Symbol">(</a><a id="52949" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="52951" class="Symbol">_</a> <a id="52953" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52956" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52959" class="Symbol">)</a> <a id="52961" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52963" class="Symbol">(</a><a id="52964" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="52978" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="52980" class="Symbol">((</a><a id="52982" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="52984" class="Symbol">_</a> <a id="52986" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="52989" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52992" class="Symbol">)</a> <a id="52994" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="52996" href="Category.Ambient.html#2115" class="Function">idC</a><a id="52999" class="Symbol">))</a> <a id="53002" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53004" class="Symbol">(</a><a id="53005" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="53007" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="53009" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53012" class="Symbol">)</a> <a id="53014" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="53017" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="53025" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="53031" class="Symbol">(</a><a id="53032" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="53036" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="53038" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="53046" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="53051" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="53060" class="Symbol">)</a> <a id="53062" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="53086" class="Symbol">(</a><a id="53087" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="53089" class="Symbol">_</a> <a id="53091" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="53094" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53097" class="Symbol">)</a> <a id="53099" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53101" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="53115" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53117" class="Symbol">(((</a><a id="53120" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="53122" class="Symbol">_</a> <a id="53124" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="53127" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53130" class="Symbol">)</a> <a id="53132" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53134" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="53136" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="53138" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53141" class="Symbol">))</a> <a id="53152" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a><a id="53153" class="Symbol">)</a>
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<a id="53171" href="Monad.Instance.K.Commutative.html#53171" class="Function">στ</a> <a id="53174" class="Symbol">:</a> <a id="53176" class="Symbol">((</a><a id="53178" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="53180" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="53183" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53186" class="Symbol">)</a> <a id="53188" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53190" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="53204" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53206" class="Symbol">(</a><a id="53207" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="53211" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="53213" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="53214" class="Symbol">))</a><a id="53216" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="53218" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53220" class="Symbol">(</a><a id="53221" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="53223" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="53225" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="53227" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53230" class="Symbol">)</a> <a id="53232" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="53234" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="53241" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="53243" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53245" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="53252" class="Symbol">(</a><a id="53253" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="53255" class="Symbol">_)</a> <a id="53258" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53260" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="53262" class="Symbol">_</a> <a id="53264" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53266" class="Symbol">(((</a><a id="53269" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="53271" class="Symbol">_</a> <a id="53273" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="53276" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53279" class="Symbol">)</a> <a id="53281" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53283" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="53284" class="Symbol">)</a> <a id="53286" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="53288" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="53290" class="Symbol">((</a><a id="53292" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="53294" class="Symbol">_</a> <a id="53296" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="53299" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53302" class="Symbol">)</a> <a id="53304" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53306" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="53307" class="Symbol">)</a> <a id="53309" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="53310" class="Symbol">)</a>
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<a id="53328" href="Monad.Instance.K.Commutative.html#53171" class="Function">στ</a> <a id="53331" class="Symbol">=</a> <a id="53333" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="53357" class="Symbol">((</a><a id="53359" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="53361" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="53364" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53367" class="Symbol">)</a> <a id="53369" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53371" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="53385" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53387" class="Symbol">(</a><a id="53388" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="53392" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="53394" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="53395" class="Symbol">))</a><a id="53397" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="53399" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53401" class="Symbol">(</a><a id="53402" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="53404" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="53406" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="53408" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53411" class="Symbol">)</a> <a id="53488" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="53491" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="53495" class="Symbol">(</a><a id="53496" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a> <a id="53509" class="Symbol">(</a><a id="53510" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="53519" class="Symbol">(</a><a id="53520" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a> <a id="53522" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="53524" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="53525" class="Symbol">))</a> <a id="53528" class="Symbol">(</a><a id="53529" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="53533" href="Monad.Instance.K.Commutative.html#57202" class="Function">by-uni</a><a id="53539" class="Symbol">))</a> <a id="53542" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="53781" class="Symbol">(((((</a><a id="53786" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="53788" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="53791" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53794" class="Symbol">)</a> <a id="53796" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53798" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="53812" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53814" class="Symbol">(</a><a id="53815" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="53817" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="53819" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53822" class="Symbol">))</a> <a id="53825" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="53827" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="53830" href="Category.Ambient.html#2115" class="Function">idC</a><a id="53833" class="Symbol">))</a> <a id="53836" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53838" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="53852" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="53854" class="Symbol">(</a><a id="53855" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="53859" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="53861" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="53862" class="Symbol">))</a> <a id="53865" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="53912" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="53916" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="53925" class="Symbol">(</a><a id="53926" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="53935" class="Symbol">_)</a> <a id="53938" class="Symbol">(</a><a id="53939" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="53945" class="Symbol">(</a><a id="53946" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="53952" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="53954" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="53963" href="Categories.Monad.Relative.html#953" class="Function">kleisliK.identityʳ</a> <a id="53982" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="53991" class="Symbol">))</a> <a id="53994" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="54014" class="Symbol">((</a><a id="54016" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="54023" class="Symbol">(((</a><a id="54026" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="54028" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54031" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54034" class="Symbol">)</a> <a id="54036" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54038" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="54052" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54054" class="Symbol">(</a><a id="54055" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="54057" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="54059" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54062" class="Symbol">))</a> <a id="54065" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="54066" class="Symbol">)</a> <a id="54068" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54071" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54074" class="Symbol">)</a> <a id="54076" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54078" class="Symbol">(</a><a id="54079" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="54081" class="Symbol">_</a> <a id="54083" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54086" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54089" class="Symbol">)</a> <a id="54091" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54093" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="54107" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54109" class="Symbol">(</a><a id="54110" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="54114" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="54116" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="54117" class="Symbol">))</a> <a id="54120" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="54145" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="54149" href="Monad.Instance.K.Commutative.html#8711" class="Function">extend-preserve</a> <a id="54165" class="Symbol">(((</a><a id="54168" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="54170" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54173" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54176" class="Symbol">)</a> <a id="54178" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54180" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="54194" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54196" class="Symbol">(</a><a id="54197" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="54199" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="54201" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54204" class="Symbol">))</a> <a id="54207" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="54208" class="Symbol">)</a> <a id="54210" class="Symbol">((</a><a id="54212" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="54214" class="Symbol">(</a><a id="54215" href="Monad.Instance.K.Commutative.html#48562" class="Bound">U</a> <a id="54217" href="Categories.Category.BinaryProd
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<a id="54283" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="54290" class="Symbol">(((</a><a id="54293" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="54295" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54298" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54301" class="Symbol">)</a> <a id="54303" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54305" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="54319" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54321" class="Symbol">(</a><a id="54322" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="54324" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="54326" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54329" class="Symbol">))</a> <a id="54332" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="54333" class="Symbol">)</a> <a id="54335" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54337" class="Symbol">((</a><a id="54339" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="54341" class="Symbol">_</a> <a id="54343" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54346" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54349" class="Symbol">)</a> <a id="54351" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54353" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="54367" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54369" class="Symbol">(</a><a id="54370" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="54374" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="54376" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="54377" class="Symbol">))</a> <a id="54380" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="54414" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="54417" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="54425" class="Symbol">(</a><a id="54426" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="54435" class="Symbol">(</a><a id="54436" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="54445" class="Symbol">_)</a> <a id="54448" class="Symbol">((</a><a id="54450" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="54459" class="Symbol">(</a><a id="54460" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="54464" class="Symbol">(</a><a id="54465" href="Monad.Instance.K.Strong.html#3312" class="Function">τ-η</a> <a id="54469" class="Symbol">_))</a> <a id="54473" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="54477" class="Symbol">)</a> <a id="54479" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="54486" class="Symbol">))</a> <a id="54489" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="54509" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="54516" class="Symbol">(((</a><a id="54519" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="54521" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54524" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54527" class="Symbol">)</a> <a id="54529" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54531" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="54545" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54547" class="Symbol">(</a><a id="54548" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="54550" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="54552" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54555" class="Symbol">))</a> <a id="54558" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="54559" class="Symbol">)</a> <a id="54561" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54563" class="Symbol">((</a><a id="54565" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="54567" class="Symbol">_</a> <a id="54569" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54571" class="Symbol">(</a><a id="54572" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="54576" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="54578" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="54580" class="Symbol">_)</a> <a id="54583" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54586" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54589" class="Symbol">)</a> <a id="54591" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54593" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="54607" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54609" class="Symbol">(</a><a id="54610" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="54614" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="54616" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="54617" class="Symbol">))</a> <a id="54620" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="54640" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="54644" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="54652" class="Symbol">(</a><a id="54653" href="Monad.Instance.K.Strong.html#5557" class="Function">τ-comm</a> <a id="54660" class="Symbol">((</a><a id="54662" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="54664" class="Symbol">(</a><a id="54665" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="54669" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="54670" class="Symbol">)</a> <a id="54672" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54675" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54678" class="Symbol">)</a> <a id="54680" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54682" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="54683" class="Symbol">)</a> <a id="54685" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="54687" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="54696" class="Symbol">(</a><a id="54697" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="54706" c
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<a id="54735" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="54742" class="Symbol">(((</a><a id="54745" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="54747" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54750" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54753" class="Symbol">)</a> <a id="54755" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54757" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="54771" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54773" class="Symbol">(</a><a id="54774" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="54776" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="54778" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54781" class="Symbol">))</a> <a id="54784" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="54785" class="Symbol">)</a> <a id="54787" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54789" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="54791" class="Symbol">_</a> <a id="54793" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54795" class="Symbol">(</a><a id="54796" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="54800" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="54802" class="Symbol">((</a><a id="54804" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="54806" class="Symbol">_</a> <a id="54808" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="54811" href="Category.Ambient.html#2115" class="Function">idC</a><a id="54814" class="Symbol">)</a> <a id="54816" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="54818" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="54819" class="Symbol">)</a><a id="54820" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="54821" class="Symbol">)</a> <a id="54866" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="54870" class="Symbol">(</a><a id="54871" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="54889" class="Symbol">(</a><a id="54890" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="54899" class="Symbol">(</a><a id="54900" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="54909" class="Symbol">_)</a> <a id="54912" class="Symbol">(</a><a id="54913" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="54919" class="Symbol">(</a><a id="54920" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="54926" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="54928" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="54937" href="Categories.Monad.Relative.html#953" class="Function">kleisliK.identityʳ</a> <a id="54956" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="54965" class="Symbol">))))</a> <a id="54970" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="54978" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="55258" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="55265" class="Symbol">(</a><a id="55266" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="55273" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="55275" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55277" class="Symbol">(((</a><a id="55280" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="55282" class="Symbol">_</a> <a id="55284" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="55287" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55290" class="Symbol">)</a> <a id="55292" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55294" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="55308" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55310" class="Symbol">(</a><a id="55311" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="55313" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="55315" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55318" class="Symbol">))</a><a id="55320" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="55321" class="Symbol">))</a> <a id="55324" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55326" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="55328" class="Symbol">_</a> <a id="55330" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55332" class="Symbol">(</a><a id="55333" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="55337" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="55339" class="Symbol">((</a><a id="55341" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="55343" class="Symbol">_</a> <a id="55345" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="55348" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55351" class="Symbol">)</a> <a id="55353" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55355" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="55356" class="Symbol">)</a> <a id="55358" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="55359" class="Symbol">)</a> <a id="55389" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="55393" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="55399" href="Categories.Monad.Relative.html#1190" class="Function">kleisliK.sym-assoc</a> <a id="55418" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="55438" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="55445" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="55447" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55449" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="55456" class="Symbol">(((</a><a id="55459" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="55461" class="Symbol">_</a> <a id="55463" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="55466" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55469" class="Symbol">)</a> <a id="55471" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55473" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="55487" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55489" class="Symbol">(</a><a id="55490" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="55492" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="55494" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55497" class="Symbol">))</a><a id="55499" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="55500" class="Symbol">)</a> <a id="55502" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55504" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="55506" class="Symbol">_</a> <a id="55508" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55510" class="Symbol">(</a><a id="55511" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="55515" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="55517" class="Symbol">((</a><a id="55519" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="55521" class="Symbol">_</a> <a id="55523" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="55526" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55529" class="Symbol">)</a> <a id="55531" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55533" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="55534" class="Symbol">)</a> <a id="55536" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="55537" class="Symbol">)</a> <a id="55569" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="55573" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="55581" class="Symbol">((</a><a id="55583" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="55601" class="Symbol">(</a><a id="55602" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="55611" class="Symbol">(</a><a id="55612" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="55621" class="Symbol">_)</a> <a id="55624" class="Symbol">(</a><a id="55625" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="55633" class="Symbol">(</a><a id="55634" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="55640" class="Symbol">(</a><a id="55641" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="55645" class="Symbol">(</a><a id="55646" href="Categories.Category.Distributive.Properties.html#4502" class="Function">distributeʳ⁻¹-natural</a> <a id="55668" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="55672" class="Symbol">(</a><a id="55673" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="55675" class="Symbol">(</a><a id="55676" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <
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<a id="55830" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="55837" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="55839" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55841" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="55848" class="Symbol">(((</a><a id="55851" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="55853" class="Symbol">_</a> <a id="55855" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="55858" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55861" class="Symbol">)</a> <a id="55863" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55865" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="55879" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55881" class="Symbol">((</a><a id="55883" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="55885" class="Symbol">(</a><a id="55886" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="55890" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a><a id="55891" class="Symbol">)</a> <a id="55893" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="55896" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55899" class="Symbol">)</a> <a id="55901" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="55903" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55906" class="Symbol">)</a> <a id="55908" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55910" class="Symbol">(</a><a id="55911" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="55913" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="55915" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55918" class="Symbol">))</a> <a id="55921" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="55922" class="Symbol">)</a> <a id="55924" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55926" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="55928" class="Symbol">_</a> <a id="55930" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55932" class="Symbol">(</a><a id="55933" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="55937" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="55939" class="Symbol">((</a><a id="55941" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="55943" class="Symbol">_</a> <a id="55945" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="55948" href="Category.Ambient.html#2115" class="Function">idC</a><a id="55951" class="Symbol">)</a> <a id="55953" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="55955" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="55956" class="Symbol">)</a> <a id="55958" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="55959" class="Symbol">)</a> <a id="55961" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="55964" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="55972" class="Symbol">(</a><a id="55973" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="55991" class="Symbol">(</a><a id="55992" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="56001" class="Symbol">(</a><a id="56002" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="56011" class="Symbol">_)</a> <a id="56014" class="Sym
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<a id="56095" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="56102" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="56104" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56106" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="56113" class="Symbol">(((</a><a id="56116" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="56118" class="Symbol">_</a> <a id="56120" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56123" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56126" class="Symbol">)</a> <a id="56128" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56130" href="Categories.Category.Distributive.html#3272" class="Function">distributeʳ⁻¹</a> <a id="56144" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56146" class="Symbol">((</a><a id="56148" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56150" class="Symbol">(</a><a id="56151" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="56155" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a><a id="56156" class="Symbol">)</a> <a id="56158" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56161" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56164" class="Symbol">)</a> <a id="56166" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56168" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="56170" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="56172" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56175" class="Symbol">))</a> <a id="56178" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="56179" class="Symbol">)</a> <a id="56181" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56183" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="56185" class="Symbol">_</a> <a id="56187" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56189" class="Symbol">(</a><a id="56190" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="56194" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="56196" class="Symbol">((</a><a id="56198" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56200" class="Symbol">_</a> <a id="56202" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56205" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56208" class="Symbol">)</a> <a id="56210" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56212" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="56213" class="Symbol">)</a> <a id="56215" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="56216" class="Symbol">)</a> <a id="56226" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="56230" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="56238" class="Symbol">((</a><a id="56240" href="Categories.Monad.Relative.html#1306" class="Function">kleisliK.extend-≈</a> <a id="56258" class="Symbol">(</a><a id="56259" href="Monad.Instance.K.Commutative.html#3465" class="Function">σ-comm</a> <a id="56266" class="Symbol">((</a><a id="56268" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56270" class="Symbol">(</a><a id="56271" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="56275" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a><a id="56276" class="Symbol">)</a> <a id="56278" href="Categories.Category.C
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<a id="56322" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="56329" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="56331" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56333" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="56340" class="Symbol">(</a><a id="56341" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="56343" class="Symbol">_</a> <a id="56345" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56347" class="Symbol">(((</a><a id="56350" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56352" class="Symbol">_</a> <a id="56354" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56357" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56360" class="Symbol">)</a> <a id="56362" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56364" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="56365" class="Symbol">)</a> <a id="56367" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="56369" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="56371" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56374" class="Symbol">))</a> <a id="56377" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56379" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="56381" class="Symbol">_</a> <a id="56383" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56385" class="Symbol">(</a><a id="56386" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="56390" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="56392" class="Symbol">((</a><a id="56394" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56396" class="Symbol">_</a> <a id="56398" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56401" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56404" class="Symbol">)</a> <a id="56406" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56408" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="56409" class="Symbol">)</a> <a id="56411" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="56412" class="Symbol">)</a> <a id="56453" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="56457" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="56465" class="Symbol">(</a><a id="56466" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="56472" class="Symbol">(</a><a id="56473" href="Category.Ambient.html#10469" class="Function">extend∘F₁</a> <a id="56483" href="Monad.Instance.K.html#1609" class="Function">monadK</a> <a id="56490" class="Symbol">(</a><a id="56491" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="56493" class="Symbol">_)</a> <a id="56496" class="Symbol">(((</a><a id="56499" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56501" class="Symbol">_</a> <a id="56503" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56506" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56509" class="Symbol">)</a> <a id="56511" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56513" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="56514" class="Symbol">)</a> <a id="56516" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="56518" href="Categories.Category.BinaryProducts.html#1465" class="Fun
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<a id="56547" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="56554" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="56556" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56558" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="56565" class="Symbol">(</a><a id="56566" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="56568" class="Symbol">_)</a> <a id="56571" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56573" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="56577" class="Symbol">(((</a><a id="56580" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56582" class="Symbol">_</a> <a id="56584" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56587" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56590" class="Symbol">)</a> <a id="56592" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56594" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="56595" class="Symbol">)</a> <a id="56597" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="56599" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="56601" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56604" class="Symbol">)</a> <a id="56606" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56608" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="56610" class="Symbol">_</a> <a id="56612" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56614" class="Symbol">(</a><a id="56615" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="56619" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="56621" class="Symbol">((</a><a id="56623" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56625" class="Symbol">_</a> <a id="56627" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56630" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56633" class="Symbol">)</a> <a id="56635" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56637" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="56638" class="Symbol">)</a> <a id="56640" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="56641" class="Symbol">)</a> <a id="56678" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="56681" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="56689" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="56697" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="56703" class="Symbol">(</a><a id="56704" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="56708" class="Symbol">(</a><a id="56709" href="Categories.NaturalTransformation.Core.html#827" class="Function">strengthen.commute</a> <a id="56728" class="Symbol">(((</a><a id="56731" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56733" class="Symbol">(</a><a id="56734" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="56738" href="Monad.Instance.K.Commutative.html#39305" class="Bound">X</a><a id="56739" class="Symbol">)</a> <a id="56741" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56744" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56747" class="Symbol">)</a> <a id="56749" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56751" href="Monad.Instance.K
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<a id="56785" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="56792" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="56794" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56796" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="56803" class="Symbol">(</a><a id="56804" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="56806" class="Symbol">_)</a> <a id="56809" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56811" class="Symbol">(</a><a id="56812" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="56814" class="Symbol">_</a> <a id="56816" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56818" class="Symbol">(((</a><a id="56821" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56823" class="Symbol">_</a> <a id="56825" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56828" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56831" class="Symbol">)</a> <a id="56833" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56835" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="56836" class="Symbol">)</a> <a id="56838" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="56840" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="56842" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="56846" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56849" class="Symbol">))</a> <a id="56852" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56854" class="Symbol">(</a><a id="56855" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="56859" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="56861" class="Symbol">((</a><a id="56863" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="56865" class="Symbol">_</a> <a id="56867" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="56870" href="Category.Ambient.html#2115" class="Function">idC</a><a id="56873" class="Symbol">)</a> <a id="56875" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="56877" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="56878" class="Symbol">)</a> <a id="56880" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="56881" class="Symbol">)</a> <a id="56916" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="56919" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="56927" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="56935" class="Symbol">(</a><a id="56936" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="56942" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="56944" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="56952" class="Symbol">(</a><a id="56953" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="56957" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="56959" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="56967" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a> <a id="56977" class="Symbol">(</a><a id="56978" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="56984" href="Categories.Functor.Core.html#511" class="Function">monadK.F.identity</a><a id="57001" class="Symbol">)))</a> <a id="57005" href="Relation.
|
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<a id="57025" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="57032" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="57034" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57036" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="57043" class="Symbol">(</a><a id="57044" href="Monad.Instance.K.Commutative.html#2998" class="Function">σ</a> <a id="57046" class="Symbol">_)</a> <a id="57049" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57051" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="57053" class="Symbol">_</a> <a id="57055" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57057" class="Symbol">(((</a><a id="57060" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="57062" class="Symbol">_</a> <a id="57064" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="57067" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57070" class="Symbol">)</a> <a id="57072" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57074" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a><a id="57075" class="Symbol">)</a> <a id="57077" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a> <a id="57079" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57081" class="Symbol">((</a><a id="57083" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="57085" class="Symbol">_</a> <a id="57087" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="57090" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57093" class="Symbol">)</a> <a id="57095" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57097" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="57098" class="Symbol">)</a> <a id="57100" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="57101" class="Symbol">)</a> <a id="57156" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="57176" class="Keyword">where</a>
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<a id="57202" href="Monad.Instance.K.Commutative.html#57202" class="Function">by-uni</a> <a id="57209" class="Symbol">:</a> <a id="57211" class="Symbol">((</a><a id="57213" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="57215" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="57218" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57221" class="Symbol">)</a> <a id="57223" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57225" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="57239" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57241" class="Symbol">(</a><a id="57242" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="57246" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57248" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="57249" class="Symbol">))</a> <a id="57252" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57254" class="Symbol">((</a><a id="57256" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="57258" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="57259" class="Symbol">)</a> <a id="57261" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57263" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57266" class="Symbol">)</a> <a id="57268" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="57270" class="Symbol">(</a><a id="57271" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="57275" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="57278" class="Symbol">(</a><a id="57279" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="57281" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="57282" class="Symbol">)</a> <a id="57284" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57286" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57289" class="Symbol">)</a> <a id="57291" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57293" class="Symbol">(</a><a id="57294" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="57296" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57298" class="Symbol">((</a><a id="57300" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="57302" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="57303" class="Symbol">)</a> <a id="57305" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57307" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57310" class="Symbol">)</a> <a id="57312" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="57315" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57318" class="Symbol">)</a> <a id="57320" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57322" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="57336" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57338" class="Symbol">(</a><a id="57339" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="57343" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57345" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="57346" class="Symbol">)</a>
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<a id="57368" href="Monad.Instance.K.Commutative.html#57202" class="Function">by-uni</a> <a id="57375" class="Symbol">=</a> <a id="57377" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="57406" class="Symbol">((</a><a id="57408" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="57410" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="57413" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57416" class="Symbol">)</a> <a id="57418" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57420" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="57434" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57436" class="Symbol">(</a><a id="57437" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="57441" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57443" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="57444" class="Symbol">))</a> <a id="57447" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57449" class="Symbol">((</a><a id="57451" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="57453" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="57454" class="Symbol">)</a> <a id="57456" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57458" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57461" class="Symbol">)</a> <a id="57488" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="57491" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="57497" class="Symbol">(</a><a id="57498" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="57504" class="Symbol">(</a><a id="57505" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="57509" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="57511" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="57519" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a> <a id="57531" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a> <a id="57539" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="57541" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="57545" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a><a id="57548" class="Symbol">))</a> <a id="57551" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="57576" class="Symbol">(</a><a id="57577" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="57579" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="57582" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57585" class="Symbol">)</a> <a id="57587" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57589" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="57603" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57605" class="Symbol">((</a><a id="57607" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="57609" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="57610" class="Symbol">)</a> <a id="57612" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57614" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57617" class="Symbol">)</a> <a id="57619" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57621" class="Symbol">(</a><a id="57622" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="57626" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57628" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="57629" class="Symbol">)</a> <a id="57658" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="57662" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="57670" class="Symbol">((</a><a id="57672" href="Categories.Category.Distributive.Properties.html#3231" class="Function">distributeˡ⁻¹-natural</a> <a id="57694" class="Symbol">(</a><a id="57695" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="57697" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="57698" class="Symbol">)</a> <a id="57700" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="57704" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="57708" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="57710" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="57718" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="57726" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="57731" class="Symbol">(</a><a id="57732" href="Category.Ambient.html#2218" class="Function">[]-unique</a> <a id="57742" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a> <a id="57754" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a><a id="57765" class="Symbol">))</a> <a id="57768" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="57776" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="57778" href="Categories.Category.Core.html#715" class="Function">assoc</a><a id="57783" class="Symbol">)</a> <a id="57785" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="57810" class="Symbol">(</a><a id="57811" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="57813" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="57816" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57819" class="Symbol">)</a> <a id="57821" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57823" class="Symbol">((((</a><a id="57827" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="57829" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="57830" class="Symbol">)</a> <a id="57832" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57834" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57837" class="Symbol">)</a> <a id="57839" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="57842" class="Symbol">((</a><a id="57844" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="57846" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="57847" class="Symbol">)</a> <a id="57849" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57851" href="Category.Ambient.html#2115" class="Function">idC</a><a id="57854" class="Symbol">))</a> <a id="57857" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57859" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="57872" class="Symbol">)</a> <a id="57874" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="57876" class="Symbol">(</a><a id="57877" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="57881" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="57883" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="57884" class="Symbol">)</a> <a id="57892" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="57895" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="57901" class="Symbol">(</a><a id="57902" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="57908" class="Symbol">(</a><a id="57909" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="57915" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="57917" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="57926" class="Symbol">(</a><a id="57927" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="57931" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="57940" class="Symbol">)</a> <a id="57942" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a> <a id="57954" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="57956" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="57960" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a><a id="57965" class="Symbol">))</a> <a id="57968" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="57993" class="Symbol">(((</a><a id="57996" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58000" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58003" class="Symbol">(</a><a id="58004" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="58006" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="58007" class="Symbol">)</a> <a id="58009" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58011" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58014" class="Symbol">)</a> <a id="58016" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58018" class="Symbol">(</a><a id="58019" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="58021" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58023" class="Symbol">((</a><a id="58025" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="58027" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="58028" class="Symbol">)</a> <a id="58030" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58032" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58035" class="Symbol">)</a> <a id="58037" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58040" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58043" class="Symbol">))</a> <a id="58046" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58048" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="58061" class="Symbol">)</a> <a id="58063" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58065" class="Symbol">(</a><a id="58066" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58070" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58072" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="58073" class="Symbol">)</a> <a id="58075" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="58078" href="Categories.Morphism.Reasoning.Core.html#1466" class="Function">assoc²</a> <a id="58085" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="58110" class="Symbol">(</a><a id="58111" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58115" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58118" class="Symbol">(</a><a id="58119" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="58121" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="58122" class="Symbol">)</a> <a id="58124" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58126" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58129" class="Symbol">)</a> <a id="58131" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58133" class="Symbol">(</a><a id="58134" href="Monad.Instance.K.Commutative.html#43446" class="Function">ψ</a> <a id="58136" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58138" class="Symbol">((</a><a id="58140" href="Monad.Instance.K.Commutative.html#48565" class="Bound">g</a> <a id="58142" href="Monad.Instance.K.Commutative.html#2896" class="Function Operator">#</a><a id="58143" class="Symbol">)</a> <a id="58145" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58147" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58150" class="Symbol">)</a> <a id="58152" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58155" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58158" class="Symbol">)</a> <a id="58160" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58162" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="58176" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58178" class="Symbol">(</a><a id="58179" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58183" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58185" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="58186" class="Symbol">)</a> <a id="58192" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="58214" href="Monad.Instance.K.Commutative.html#58214" class="Function">comm</a> <a id="58219" class="Symbol">:</a> <a id="58221" class="Symbol">(</a><a id="58222" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="58224" class="Symbol">_</a> <a id="58226" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58229" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58232" class="Symbol">)</a> <a id="58234" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58236" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="58250" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58252" class="Symbol">(</a><a id="58253" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58257" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58259" class="Symbol">(</a><a id="58260" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="58262" class="Symbol">_</a> <a id="58264" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58267" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58270" class="Symbol">)</a> <a id="58272" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58274" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="58275" class="Symbol">)</a> <a id="58277" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="58279" class="Symbol">(</a><a id="58280" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="58282" class="Symbol">_</a> <a id="58284" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58286" class="Symbol">(</a><a id="58287" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58291" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58293" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="58295" class="Symbol">_)</a> <a id="58298" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58301" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58304" class="Symbol">)</a> <a id="58306" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58308" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="58322" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58324" class="Symbol">(</a><a id="58325" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58329" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58331" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="58332" class="Symbol">)</a>
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<a id="58354" href="Monad.Instance.K.Commutative.html#58214" class="Function">comm</a> <a id="58359" class="Symbol">=</a> <a id="58361" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="58365" class="Symbol">(</a><a id="58366" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="58395" class="Symbol">(</a><a id="58396" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="58398" class="Symbol">_</a> <a id="58400" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58402" class="Symbol">(</a><a id="58403" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58407" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58409" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="58411" class="Symbol">_)</a> <a id="58414" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58417" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58420" class="Symbol">)</a> <a id="58422" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58424" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="58438" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58440" class="Symbol">(</a><a id="58441" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58445" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58447" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="58448" class="Symbol">)</a> <a id="58461" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="58465" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="58471" class="Symbol">(</a><a id="58472" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="58478" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="58480" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="58489" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="58494" href="Categories.Category.Core.html#1339" class="Function">identity²</a><a id="58503" class="Symbol">)</a> <a id="58505" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="58530" class="Symbol">(</a><a id="58531" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="58533" class="Symbol">_</a> <a id="58535" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58538" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58541" class="Symbol">)</a> <a id="58543" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58545" class="Symbol">((</a><a id="58547" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58551" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58553" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="58555" class="Symbol">_)</a> <a id="58558" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58561" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58564" class="Symbol">)</a> <a id="58566" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58568" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="58582" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58584" class="Symbol">(</a><a id="58585" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58589" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58591" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="58592" class="Symbol">)</a> <a id="58596" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="58599" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="58607" class="Symbol">(</a><a id="58608" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="58614" class="Symbol">((</a><a id="58616" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="58625" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="58630" class="Symbol">(</a><a id="58631" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="58635" class="Symbol">(</a><a id="58636" href="Category.Ambient.html#2592" class="Function">⟨⟩-unique</a> <a id="58646" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a> <a id="58654" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a><a id="58661" class="Symbol">)))</a> <a id="58665" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="58673" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="58675" href="Categories.Category.Distributive.Properties.html#3231" class="Function">distributeˡ⁻¹-natural</a> <a id="58697" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58701" class="Symbol">(</a><a id="58702" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="58704" class="Symbol">(</a><a id="58705" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="58709" href="Monad.Instance.K.Commutative.html#39309" class="Bound">Y</a><a id="58710" class="Symbol">))</a> <a id="58713" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58716" class="Symbol">))</a> <a id="58719" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="58744" class="Symbol">(</a><a id="58745" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="58747" class="Symbol">_</a> <a id="58749" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58752" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58755" class="Symbol">)</a> <a id="58757" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58759" class="Symbol">(</a><a id="58760" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="58774" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58776" class="Symbol">(</a><a id="58777" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58781" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58783" class="Symbol">(</a><a id="58784" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="58786" class="Symbol">_</a> <a id="58788" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58791" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58794" class="Symbol">)))</a> <a id="58798" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58800" class="Symbol">(</a><a id="58801" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58805" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58807" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="58808" class="Symbol">)</a> <a id="58810" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="58813" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="58821" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="58827" class="Symbol">(</a><a id="58828" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="58832" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="58834" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="58842" href="Categories.Category.Core.html#1339" class="Function">identity²</a> <a id="58852" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="58856" class="Symbol">)</a> <a id="58858" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="58883" class="Symbol">(</a><a id="58884" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="58886" class="Symbol">_</a> <a id="58888" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58891" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58894" class="Symbol">)</a> <a id="58896" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58898" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="58912" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58914" class="Symbol">(</a><a id="58915" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="58919" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="58921" class="Symbol">(</a><a id="58922" href="Monad.Instance.K.Commutative.html#2660" class="Function">η</a> <a id="58924" class="Symbol">_</a> <a id="58926" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="58929" href="Category.Ambient.html#2115" class="Function">idC</a><a id="58932" class="Symbol">)</a> <a id="58934" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="58936" href="Monad.Instance.K.Commutative.html#42732" class="Bound">h</a><a id="58937" class="Symbol">)</a> <a id="58949" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a><a id="58950" class="Symbol">)</a>
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</pre>
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