bsc-leon-vatthauer/agda/bsc-thesis/Monad.Instance.K.Strong.md

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<a id="617" class="Keyword">import</a> <a id="624" href="Monad.Instance.K.html" class="Module">Monad.Instance.K</a> <a id="641" class="Symbol">as</a> <a id="644" class="Module">MIK</a>
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<pre class="Agda"><a id="665" class="Keyword">module</a> <a id="672" href="Monad.Instance.K.Strong.html" class="Module">Monad.Instance.K.Strong</a> <a id="696" class="Symbol">{</a><a id="697" href="Monad.Instance.K.Strong.html#697" class="Bound">o</a> <a id="699" href="Monad.Instance.K.Strong.html#699" class="Bound">ℓ</a> <a id="701" href="Monad.Instance.K.Strong.html#701" class="Bound">e</a><a id="702" class="Symbol">}</a> <a id="704" class="Symbol">(</a><a id="705" href="Monad.Instance.K.Strong.html#705" class="Bound">ambient</a> <a id="713" class="Symbol">:</a> <a id="715" href="Category.Ambient.html#1681" class="Record">Ambient</a> <a id="723" href="Monad.Instance.K.Strong.html#697" class="Bound">o</a> <a id="725" href="Monad.Instance.K.Strong.html#699" class="Bound">ℓ</a> <a id="727" href="Monad.Instance.K.Strong.html#701" class="Bound">e</a><a id="728" class="Symbol">)</a> <a id="730" class="Symbol">(</a><a id="731" href="Monad.Instance.K.Strong.html#731" class="Bound">MK</a> <a id="734" class="Symbol">:</a> <a id="736" href="Monad.Instance.K.html#1123" class="Record">MIK.MonadK</a> <a id="747" href="Monad.Instance.K.Strong.html#705" class="Bound">ambient</a><a id="754" class="Symbol">)</a> <a id="756" class="Keyword">where</a>
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</pre>

# The monad K is strong

K is a strong monad with the strength defined as `η ♯`, where ♯ is the operator we get from stability.
Verifying the axioms of strength is straightforward once you know the procedure, since the proofs are all very similar.

For example the proof of `identityˡ` i.e. `K₁ π₂ ∘ τ ≈ π₂` goes as follows:

1. find a morphism `f` such that `K₁ π₂ ∘ τ ≈ f ♯ ≈ π₂`
2. show that `K₁ π₂ ∘ τ` is iteration preserving and satisfies the stabiltiy law
3. show that `π₂` is iteration preserving and satisfies the stabiltiy law

=> by uniqueness of `f ♯` we are done

The following diagram demonstrates this:

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<pre class="Agda">  <a id="2583" class="Comment">-- we use properties of the kleisli representation as well as the &#39;normal&#39; monad representation</a>
  <a id="2681" class="Keyword">open</a> <a id="2686" href="Monad.Instance.K.html#1775" class="Module">kleisliK</a> <a id="2695" class="Keyword">using</a> <a id="2701" class="Symbol">(</a><a id="2702" href="Categories.Monad.Relative.html#895" class="Function">extend</a><a id="2708" class="Symbol">)</a>
  <a id="2712" class="Keyword">open</a> <a id="2717" href="Monad.Instance.K.html#1672" class="Module">monadK</a> <a id="2724" class="Keyword">using</a> <a id="2730" class="Symbol">(</a><a id="2731" href="Categories.Monad.html#583" class="Function">μ</a><a id="2732" class="Symbol">)</a>

  <a id="2737" class="Comment">-- defining τ</a>
  <a id="2753" class="Keyword">private</a>
    <a id="2765" class="Comment">-- some helper definitions to make our life easier</a>
    <a id="η"></a><a id="2820" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="2822" class="Symbol">=</a> <a id="2824" class="Symbol">λ</a> <a id="2826" href="Monad.Instance.K.Strong.html#2826" class="Bound">Z</a> <a id="2828" class="Symbol">→</a> <a id="2830" href="Categories.FreeObjects.Free.html#854" class="Field">FreeObject.η</a> <a id="2843" class="Symbol">(</a><a id="2844" href="Monad.Instance.K.html#1182" class="Field">freealgebras</a> <a id="2857" href="Monad.Instance.K.Strong.html#2826" class="Bound">Z</a><a id="2858" class="Symbol">)</a>
    <a id="_♯"></a><a id="2864" href="Monad.Instance.K.Strong.html#2864" class="Function Operator">_♯</a> <a id="2867" class="Symbol">=</a> <a id="2869" class="Symbol">λ</a> <a id="2871" class="Symbol">{</a><a id="2872" href="Monad.Instance.K.Strong.html#2872" class="Bound">A</a> <a id="2874" href="Monad.Instance.K.Strong.html#2874" class="Bound">X</a> <a id="2876" href="Monad.Instance.K.Strong.html#2876" class="Bound">Y</a><a id="2877" class="Symbol">}</a> <a id="2879" href="Monad.Instance.K.Strong.html#2879" class="Bound">f</a> <a id="2881" class="Symbol">→</a> <a id="2883" href="Algebra.Elgot.Stable.html#2658" class="Field Operator">IsStableFreeElgotAlgebra.[_,_]♯</a> <a id="2915" class="Symbol">{</a><a id="2916" class="Argument">Y</a> <a id="2918" class="Symbol">=</a> <a id="2920" href="Monad.Instance.K.Strong.html#2874" class="Bound">X</a><a id="2921" class="Symbol">}</a> <a id="2923" class="Symbol">(</a><a id="2924" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="2931" href="Monad.Instance.K.Strong.html#2874" class="Bound">X</a><a id="2932" class="Symbol">)</a> <a id="2934" class="Symbol">{</a><a id="2935" class="Argument">X</a> <a id="2937" class="Symbol">=</a> <a id="2939" href="Monad.Instance.K.Strong.html#2872" class="Bound">A</a><a id="2940" class="Symbol">}</a> <a id="2942" class="Symbol">(</a><a id="2943" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="2952" href="Monad.Instance.K.Strong.html#2876" class="Bound">Y</a><a id="2953" class="Symbol">)</a> <a id="2955" href="Monad.Instance.K.Strong.html#2879" class="Bound">f</a>
    <a id="_#"></a><a id="2961" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">_#</a> <a id="2964" class="Symbol">=</a> <a id="2966" class="Symbol">λ</a> <a id="2968" class="Symbol">{</a><a id="2969" href="Monad.Instance.K.Strong.html#2969" class="Bound">A</a><a id="2970" class="Symbol">}</a> <a id="2972" class="Symbol">{</a><a id="2973" href="Monad.Instance.K.Strong.html#2973" class="Bound">X</a><a id="2974" class="Symbol">}</a> <a id="2976" href="Monad.Instance.K.Strong.html#2976" class="Bound">f</a> <a id="2978" class="Symbol">→</a> <a id="2980" href="Algebra.Elgot.html#1938" class="Function Operator">Elgot-Algebra._#</a> <a id="2997" class="Symbol">(</a><a id="2998" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="3007" href="Monad.Instance.K.Strong.html#2969" class="Bound">A</a><a id="3008" class="Symbol">)</a> <a id="3010" class="Symbol">{</a><a id="3011" class="Argument">X</a> <a id="3013" class="Symbol">=</a> <a id="3015" href="Monad.Instance.K.Strong.html#2973" class="Bound">X</a><a id="3016" class="Symbol">}</a> <a id="3018" href="Monad.Instance.K.Strong.html#2976" class="Bound">f</a>

  <a id="3023" class="Keyword">open</a> <a id="3028" href="Algebra.Elgot.Stable.html#2437" class="Module">IsStableFreeElgotAlgebra</a> <a id="3053" class="Keyword">using</a> <a id="3059" class="Symbol">(</a><a id="3060" href="Algebra.Elgot.Stable.html#2784" class="Field">♯-law</a><a id="3065" class="Symbol">;</a> <a id="3067" href="Algebra.Elgot.Stable.html#2892" class="Field">♯-preserving</a><a id="3079" class="Symbol">;</a> <a id="3081" href="Algebra.Elgot.Stable.html#3117" class="Field">♯-unique</a><a id="3089" class="Symbol">)</a>
  <a id="3093" class="Keyword">open</a> <a id="3098" href="Algebra.Elgot.html#15964" class="Module">Elgot-Algebra</a> <a id="3112" class="Keyword">using</a> <a id="3118" class="Symbol">(</a><a id="3119" href="Algebra.Elgot.html#2086" class="Function">#-Uniformity</a><a id="3131" class="Symbol">;</a> <a id="3133" href="Algebra.Elgot.html#2011" class="Function">#-Fixpoint</a><a id="3143" class="Symbol">;</a> <a id="3145" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a><a id="3153" class="Symbol">)</a>

  <a id="3158" class="Keyword">module</a> <a id="3165" href="Monad.Instance.K.Strong.html#3165" class="Module">_</a> <a id="3167" class="Symbol">(</a><a id="3168" href="Monad.Instance.K.Strong.html#3168" class="Bound">P</a> <a id="3170" class="Symbol">:</a> <a id="3172" href="Categories.Category.Core.html#559" class="Field">Category.Obj</a> <a id="3185" class="Symbol">(</a><a id="3186" href="Monad.Instance.K.Strong.html#142" class="Function">CProduct</a> <a id="3195" href="Category.Ambient.html#1757" class="Function">C</a> <a id="3197" href="Category.Ambient.html#1757" class="Function">C</a><a id="3198" class="Symbol">))</a> <a id="3201" class="Keyword">where</a>
    <a id="3211" class="Keyword">private</a>
      <a id="3225" href="Monad.Instance.K.Strong.html#3225" class="Function">X</a> <a id="3227" class="Symbol">=</a> <a id="3229" href="Data.Product.Base.html#636" class="Field">proj₁</a> <a id="3235" href="Monad.Instance.K.Strong.html#3168" class="Bound">P</a>
      <a id="3243" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a> <a id="3245" class="Symbol">=</a> <a id="3247" href="Data.Product.Base.html#650" class="Field">proj₂</a> <a id="3253" href="Monad.Instance.K.Strong.html#3168" class="Bound">P</a>
    <a id="3259" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="3261" class="Symbol">:</a> <a id="3263" href="Monad.Instance.K.Strong.html#3225" class="Function">X</a> <a id="3265" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="3267" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="3271" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a> <a id="3273" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="3275" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="3279" class="Symbol">(</a><a id="3280" href="Monad.Instance.K.Strong.html#3225" class="Function">X</a> <a id="3282" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="3284" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a><a id="3285" class="Symbol">)</a>
    <a id="3291" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="3293" class="Symbol">=</a> <a id="3295" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3297" class="Symbol">(</a><a id="3298" href="Monad.Instance.K.Strong.html#3225" class="Function">X</a> <a id="3300" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="3302" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a><a id="3303" class="Symbol">)</a> <a id="3305" href="Monad.Instance.K.Strong.html#2864" class="Function Operator">♯</a>

    <a id="3312" href="Monad.Instance.K.Strong.html#3312" class="Function">τ-η</a> <a id="3316" class="Symbol">:</a> <a id="3318" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="3320" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3322" class="Symbol">(</a><a id="3323" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="3327" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3329" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3331" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a><a id="3332" class="Symbol">)</a> <a id="3334" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3336" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3338" class="Symbol">(</a><a id="3339" href="Monad.Instance.K.Strong.html#3225" class="Function">X</a> <a id="3341" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="3343" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a><a id="3344" class="Symbol">)</a>
    <a id="3350" href="Monad.Instance.K.Strong.html#3312" class="Function">τ-η</a> <a id="3354" class="Symbol">=</a> <a id="3356" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="3360" class="Symbol">(</a><a id="3361" href="Algebra.Elgot.Stable.html#2784" class="Field">♯-law</a> <a id="3367" class="Symbol">(</a><a id="3368" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="3375" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a><a id="3376" class="Symbol">)</a> <a id="3378" class="Symbol">(</a><a id="3379" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3381" class="Symbol">(</a><a id="3382" href="Monad.Instance.K.Strong.html#3225" class="Function">X</a> <a id="3384" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="3386" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a><a id="3387" class="Symbol">)))</a>

    <a id="3396" class="Comment">-- for K not only strengthening with 1 is irrelevant</a>
    <a id="3453" href="Monad.Instance.K.Strong.html#3453" class="Function">τ-π₂</a> <a id="3458" class="Symbol">:</a> <a id="3460" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3464" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="3467" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3469" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="3471" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3473" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a>
    <a id="3480" href="Monad.Instance.K.Strong.html#3453" class="Function">τ-π₂</a> <a id="3485" class="Symbol">=</a> <a id="3487" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a> 
      <a id="3500" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3504" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="3507" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3509" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="3511" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3514" href="Algebra.Elgot.Stable.html#3117" class="Field">♯-unique</a> <a id="3523" class="Symbol">(</a><a id="3524" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="3531" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a><a id="3532" class="Symbol">)</a> <a id="3534" class="Symbol">(</a><a id="3535" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3537" class="Symbol">_</a> <a id="3539" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3541" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="3543" class="Symbol">)</a> <a id="3545" class="Symbol">(</a><a id="3546" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3550" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="3553" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3555" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a><a id="3556" class="Symbol">)</a> <a id="3558" href="Monad.Instance.K.Strong.html#3684" class="Function">comm₁</a> <a id="3564" href="Monad.Instance.K.Strong.html#4052" class="Function">comm₂</a> <a id="3570" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
      <a id="3578" class="Symbol">(</a><a id="3579" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3581" class="Symbol">_</a> <a id="3583" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3585" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="3587" class="Symbol">)</a> <a id="3589" href="Monad.Instance.K.Strong.html#2864" class="Function Operator">♯</a> <a id="3591" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3594" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="3598" class="Symbol">(</a><a id="3599" href="Algebra.Elgot.Stable.html#3117" class="Field">♯-unique</a> <a id="3608" class="Symbol">(</a><a id="3609" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="3616" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a><a id="3617" class="Symbol">)</a> <a id="3619" class="Symbol">(</a><a id="3620" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3622" class="Symbol">_</a> <a id="3624" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3626" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="3628" class="Symbol">)</a> <a id="3630" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="3633" class="Symbol">(</a><a id="3634" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="3638" href="Categories.Category.BinaryProducts.html#2453" class="Function">π₂∘⁂</a><a id="3642" class="Symbol">)</a> <a id="3644" href="Monad.Instance.K.Strong.html#4699" class="Function">comm₃</a><a id="3649" class="Symbol">)</a> <a id="3651" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
      <a id="3659" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="3662" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
      <a id="3670" class="Keyword">where</a>
        <a id="3684" href="Monad.Instance.K.Strong.html#3684" class="Function">comm₁</a> <a id="3690" class="Symbol">:</a> <a id="3692" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3694" class="Symbol">_</a> <a id="3696" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3698" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="3701" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="3703" class="Symbol">(</a><a id="3704" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3708" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="3711" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3713" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a><a id="3714" class="Symbol">)</a> <a id="3716" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3718" class="Symbol">(</a><a id="3719" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="3723" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3725" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3727" class="Symbol">_)</a>
        <a id="3738" href="Monad.Instance.K.Strong.html#3684" class="Function">comm₁</a> <a id="3744" class="Symbol">=</a> <a id="3746" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="3750" class="Symbol">(</a><a id="3751" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a> 
          <a id="3768" class="Symbol">(</a><a id="3769" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3773" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="3776" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3778" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a><a id="3779" class="Symbol">)</a> <a id="3781" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3783" class="Symbol">(</a><a id="3784" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="3788" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="3790" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3792" class="Symbol">_)</a> <a id="3795" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3798" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="3804" href="Monad.Instance.K.Strong.html#3312" class="Function">τ-η</a> <a id="3808" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
          <a id="3821" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="3825" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="3828" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3830" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3832" class="Symbol">_</a>                 <a id="3850" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3853" class="Symbol">(</a><a id="3854" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="3858" class="Symbol">(</a><a id="3859" href="Category.Ambient.html#10091" class="Function">F₁⇒extend</a> <a id="3869" href="Monad.Instance.K.html#1609" class="Function">monadK</a> <a id="3876" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="3878" class="Symbol">))</a> <a id="3881" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="3889" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
          <a id="3901" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="3908" class="Symbol">(</a><a id="3909" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3911" class="Symbol">_</a> <a id="3913" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3915" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a><a id="3917" class="Symbol">)</a> <a id="3919" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3921" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3923" class="Symbol">_</a>                              <a id="3954" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3957" href="Categories.Monad.Relative.html#953" class="Function">kleisliK.identityʳ</a> <a id="3976" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
          <a id="3988" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="3990" class="Symbol">_</a> <a id="3992" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="3994" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a>                                             <a id="4041" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a><a id="4042" class="Symbol">)</a>
        <a id="4052" href="Monad.Instance.K.Strong.html#4052" class="Function">comm₂</a> <a id="4058" class="Symbol">:</a> <a id="4060" class="Symbol">∀</a> <a id="4062" class="Symbol">{</a><a id="4063" href="Monad.Instance.K.Strong.html#4063" class="Bound">Z</a> <a id="4065" class="Symbol">:</a> <a id="4067" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="4070" class="Symbol">}</a> <a id="4072" class="Symbol">(</a><a id="4073" href="Monad.Instance.K.Strong.html#4073" class="Bound">h</a> <a id="4075" class="Symbol">:</a> <a id="4077" href="Monad.Instance.K.Strong.html#4063" class="Bound">Z</a> <a id="4079" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="4081" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="4085" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a> <a id="4087" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="4089" href="Monad.Instance.K.Strong.html#4063" class="Bound">Z</a><a id="4090" class="Symbol">)</a> <a id="4092" class="Symbol">→</a> <a id="4094" class="Symbol">(</a><a id="4095" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="4099" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="4102" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4104" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a><a id="4105" class="Symbol">)</a> <a id="4107" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4109" class="Symbol">(</a><a id="4110" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="4114" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4116" href="Monad.Instance.K.Strong.html#4073" class="Bound">h</a> <a id="4118" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a> <a id="4120" class="Symbol">)</a> <a id="4122" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="4124" class="Symbol">((</a><a id="4126" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="4130" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="4133" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4135" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="4137" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="4140" href="Category.Ambient.html#2115" class="Function">idC</a><a id="4143" class="Symbol">)</a> <a id="4145" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4147" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="4161" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4163" class="Symbol">(</a><a id="4164" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="4168" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4170" href="Monad.Instance.K.Strong.html#4073" class="Bound">h</a><a id="4171" class="Symbol">))</a><a id="4173" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a>
        <a id="4183" href="Monad.Instance.K.Strong.html#4052" class="Function">comm₂</a> <a id="4189" class="Symbol">{</a><a id="4190" href="Monad.Instance.K.Strong.html#4190" class="Bound">Z</a><a id="4191" class="Symbol">}</a> <a id="4193" href="Monad.Instance.K.Strong.html#4193" class="Bound">h</a> <a id="4195" class="Symbol">=</a> <a id="4197" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
          <a id="4213" class="Symbol">(</a><a id="4214" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="4218" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="4221" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4223" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a><a id="4224" class="Symbol">)</a> <a id="4226" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="4228" class="Symbol">(</a><a id="4229" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="4233" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="4235" href="Monad.Instance.K.Strong.html#4193" class="Bound">h</a> <a id="4237" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a><a id="4238" class="Symbol">)</a>                                   <a id="4274" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="4277" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="4283" class="Symbol">(</a><a id="4284" href="Algebra.Elgot.Stable.html#2892" class="Field">♯-preserving</a> <a id="4297" class="Symbol">(</a><a id="4298" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="4305" href="Monad.Instance.K.Strong.html#3243" class="Function">Y</a><a id="4306" class="Symbol">)</a> <a id="4308" class="Symbol">(</a><a id="4309" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="4311" class="Symbol">_)</a> <a id="4314" href="Monad.Instance.K.Strong.html#4193" class="Bound">h</a><a id="4315" class="Symbol">)</a> <a id="4317" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
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              <a id="5498" href="Monad.Instance.K.Strong.html#4822" class="Bound">h</a> <a id="5500" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5502" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a>                                                <a id="5552" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>

  <a id="τ-comm"></a><a id="5557" href="Monad.Instance.K.Strong.html#5557" class="Function">τ-comm</a> <a id="5564" class="Symbol">:</a> <a id="5566" class="Symbol">∀</a> <a id="5568" class="Symbol">{</a><a id="5569" href="Monad.Instance.K.Strong.html#5569" class="Bound">X</a> <a id="5571" href="Monad.Instance.K.Strong.html#5571" class="Bound">Y</a> <a id="5573" href="Monad.Instance.K.Strong.html#5573" class="Bound">Z</a> <a id="5575" class="Symbol">:</a> <a id="5577" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="5580" class="Symbol">}</a> <a id="5582" class="Symbol">(</a><a id="5583" href="Monad.Instance.K.Strong.html#5583" class="Bound">h</a> <a id="5585" class="Symbol">:</a> <a id="5587" href="Monad.Instance.K.Strong.html#5573" class="Bound">Z</a> <a id="5589" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="5591" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="5595" href="Monad.Instance.K.Strong.html#5571" class="Bound">Y</a> <a id="5597" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="5599" href="Monad.Instance.K.Strong.html#5573" class="Bound">Z</a><a id="5600" class="Symbol">)</a> <a id="5602" class="Symbol">→</a> <a id="5604" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="5606" class="Symbol">(</a><a id="5607" href="Monad.Instance.K.Strong.html#5569" class="Bound">X</a> <a id="5609" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="5611" href="Monad.Instance.K.Strong.html#5571" class="Bound">Y</a><a id="5612" class="Symbol">)</a> <a id="5614" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5616" class="Symbol">(</a><a id="5617" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="5621" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5623" href="Monad.Instance.K.Strong.html#5583" class="Bound">h</a> <a id="5625" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a><a id="5626" class="Symbol">)</a> <a id="5628" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="5630" class="Symbol">((</a><a id="5632" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="5634" class="Symbol">(</a><a id="5635" href="Monad.Instance.K.Strong.html#5569" class="Bound">X</a> <a id="5637" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="5639" href="Monad.Instance.K.Strong.html#5571" class="Bound">Y</a><a id="5640" class="Symbol">)</a> <a id="5642" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="5645" href="Category.Ambient.html#2115" class="Function">idC</a><a id="5648" class="Symbol">)</a> <a id="5650" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5652" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="5666" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5668" class="Symbol">(</a><a id="5669" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="5673" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="5675" href="Monad.Instance.K.Strong.html#5583" class="Bound">h</a><a id="5676" class="Symbol">))</a><a id="5678" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a>
  <a id="5682" href="Monad.Instance.K.Strong.html#5557" class="Function">τ-comm</a> <a id="5689" class="Symbol">{</a><a id="5690" href="Monad.Instance.K.Strong.html#5690" class="Bound">X</a><a id="5691" class="Symbol">}</a> <a id="5693" class="Symbol">{</a><a id="5694" href="Monad.Instance.K.Strong.html#5694" class="Bound">Y</a><a id="5695" class="Symbol">}</a> <a id="5697" class="Symbol">{</a><a id="5698" href="Monad.Instance.K.Strong.html#5698" class="Bound">Z</a><a id="5699" class="Symbol">}</a> <a id="5701" href="Monad.Instance.K.Strong.html#5701" class="Bound">h</a> <a id="5703" class="Symbol">=</a> <a id="5705" href="Algebra.Elgot.Stable.html#2892" class="Field">♯-preserving</a> <a id="5718" class="Symbol">(</a><a id="5719" href="Monad.Instance.K.html#1228" class="Field">stable</a> <a id="5726" href="Monad.Instance.K.Strong.html#5694" class="Bound">Y</a><a id="5727" class="Symbol">)</a> <a id="5729" class="Symbol">(</a><a id="5730" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="5732" class="Symbol">(</a><a id="5733" href="Monad.Instance.K.Strong.html#5690" class="Bound">X</a> <a id="5735" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="5737" href="Monad.Instance.K.Strong.html#5694" class="Bound">Y</a><a id="5738" class="Symbol">))</a> <a id="5741" href="Monad.Instance.K.Strong.html#5701" class="Bound">h</a>

  <a id="K₁η"></a><a id="5746" href="Monad.Instance.K.Strong.html#5746" class="Function">K₁η</a> <a id="5750" class="Symbol">:</a> <a id="5752" class="Symbol">∀</a> <a id="5754" class="Symbol">{</a><a id="5755" href="Monad.Instance.K.Strong.html#5755" class="Bound">X</a> <a id="5757" href="Monad.Instance.K.Strong.html#5757" class="Bound">Y</a><a id="5758" class="Symbol">}</a> <a id="5760" class="Symbol">(</a><a id="5761" href="Monad.Instance.K.Strong.html#5761" class="Bound">f</a> <a id="5763" class="Symbol">:</a> <a id="5765" href="Monad.Instance.K.Strong.html#5755" class="Bound">X</a> <a id="5767" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="5769" href="Monad.Instance.K.Strong.html#5757" class="Bound">Y</a><a id="5770" class="Symbol">)</a> <a id="5772" class="Symbol">→</a> <a id="5774" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5778" href="Monad.Instance.K.Strong.html#5761" class="Bound">f</a> <a id="5780" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5782" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="5784" href="Monad.Instance.K.Strong.html#5755" class="Bound">X</a> <a id="5786" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="5788" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="5790" href="Monad.Instance.K.Strong.html#5757" class="Bound">Y</a> <a id="5792" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5794" href="Monad.Instance.K.Strong.html#5761" class="Bound">f</a>
  <a id="5798" href="Monad.Instance.K.Strong.html#5746" class="Function">K₁η</a> <a id="5802" class="Symbol">{</a><a id="5803" href="Monad.Instance.K.Strong.html#5803" class="Bound">X</a><a id="5804" class="Symbol">}</a> <a id="5806" class="Symbol">{</a><a id="5807" href="Monad.Instance.K.Strong.html#5807" class="Bound">Y</a><a id="5808" class="Symbol">}</a> <a id="5810" href="Monad.Instance.K.Strong.html#5810" class="Bound">f</a> <a id="5812" class="Symbol">=</a> <a id="5814" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a> 
    <a id="5825" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="5829" href="Monad.Instance.K.Strong.html#5810" class="Bound">f</a> <a id="5831" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5833" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="5835" href="Monad.Instance.K.Strong.html#5803" class="Bound">X</a>            <a id="5848" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5851" class="Symbol">(</a><a id="5852" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="5856" class="Symbol">(</a><a id="5857" href="Category.Ambient.html#10091" class="Function">F₁⇒extend</a> <a id="5867" href="Monad.Instance.K.html#1609" class="Function">monadK</a> <a id="5874" href="Monad.Instance.K.Strong.html#5810" class="Bound">f</a><a id="5875" class="Symbol">))</a> <a id="5878" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="5886" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
    <a id="5893" href="Categories.Monad.Relative.html#895" class="Function">extend</a> <a id="5900" class="Symbol">(</a><a id="5901" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="5903" href="Monad.Instance.K.Strong.html#5807" class="Bound">Y</a> <a id="5905" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5907" href="Monad.Instance.K.Strong.html#5810" class="Bound">f</a><a id="5908" class="Symbol">)</a> <a id="5910" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5912" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="5914" href="Monad.Instance.K.Strong.html#5803" class="Bound">X</a> <a id="5916" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="5919" href="Categories.Monad.Relative.html#953" class="Function">kleisliK.identityʳ</a> <a id="5938" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
    <a id="5945" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="5947" href="Monad.Instance.K.Strong.html#5807" class="Bound">Y</a> <a id="5949" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="5951" href="Monad.Instance.K.Strong.html#5810" class="Bound">f</a>                <a id="5968" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>

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                <a id="9060" class="Symbol">((</a><a id="9062" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="9064" class="Symbol">(</a><a id="9065" href="Monad.Instance.K.Strong.html#6515" class="Bound">W</a> <a id="9067" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="9069" href="Monad.Instance.K.Strong.html#6519" class="Bound">X</a><a id="9070" class="Symbol">)</a> <a id="9072" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9075" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9078" class="Symbol">)</a> <a id="9080" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9082" class="Symbol">((</a><a id="9084" href="Monad.Instance.K.Strong.html#6524" class="Bound">f</a> <a id="9086" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="9088" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="9092" href="Monad.Instance.K.Strong.html#6528" class="Bound">g</a><a id="9093" class="Symbol">)</a> <a id="9095" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="9098" class="Symbol">(</a><a id="9099" href="Monad.Instance.K.Strong.html#6524" class="Bound">f</a> <a id="9101" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="9103" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9106" class="Symbol">)))</a> <a id="9110" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9112" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="9126" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9128" class="Symbol">(</a><a id="9129" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="9133" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="9135" href="Monad.Instance.K.Strong.html#7768" class="Bound">h</a><a id="9136" class="Symbol">)</a>   <a id="9140" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="9143" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="9149" class="Symbol">(</a><a id="9150" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="9156" class="Symbol">(</a><a id="9157" href="Categories.Category.Distributive.Properties.html#3231" class="Function">distributeˡ⁻¹-natural</a> <a id="9179" href="Monad.Instance.K.Strong.html#6524" class="Bound">f</a> <a id="9181" class="Symbol">(</a><a id="9182" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="9186" href="Monad.Instance.K.Strong.html#6528" class="Bound">g</a><a id="9187" class="Symbol">)</a> <a id="9189" href="Category.Ambient.html#2115" class="Function">idC</a><a id="9192" class="Symbol">))</a> <a id="9195" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
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            <a id="11557" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="11561" class="Symbol">_</a> <a id="11563" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11565" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="11569" class="Symbol">(</a><a id="11570" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="11572" class="Symbol">_)</a> <a id="11575" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11577" class="Symbol">(((</a><a id="11580" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="11582" class="Symbol">(</a><a id="11583" href="Monad.Instance.K.Strong.html#10430" class="Bound">A</a> <a id="11585" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="11587" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="11591" href="Monad.Instance.K.Strong.html#10434" class="Bound">B</a><a id="11592" class="Symbol">)</a> <a id="11594" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="11597" href="Category.Ambient.html#2115" class="Function">idC</a><a id="11600" class="Symbol">)</a> <a id="11602" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11604" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="11618" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11620" class="Symbol">(</a><a id="11621" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="11625" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="11627" href="Monad.Instance.K.Strong.html#11398" class="Bound">h</a><a id="11628" class="Symbol">))</a> <a id="11631" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a><a id="11632" class="Symbol">)</a>                 <a id="11650" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="11653" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="11661" class="Symbol">(</a><a id="11662" href="Category.Construction.ElgotAlgebras.html#812" class="Field">Elgot-Algebra-Morphism.preserves</a> <a id="11695" class="Symbol">(((</a><a id="11698" href="Monad.Instance.K.html#1182" class="Field">freealgebras</a> <a id="11711" class="Symbol">_)</a> <a id="11714" href="Categories.FreeObjects.Free.html#880" class="Field Operator">FreeObject.*</a><a id="11726" class="Symbol">)</a> <a id="11728" class="Symbol">(</a><a id="11729" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="11731" class="Symbol">_</a> <a id="11733" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11735" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="11737" class="Symbol">_)))</a> <a id="11742" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
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            <a id="11939" class="Symbol">((</a><a id="11941" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="11945" class="Symbol">_</a> <a id="11947" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="11950" href="Category.Ambient.html#2115" class="Function">idC</a><a id="11953" class="Symbol">)</a> <a id="11955" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11957" class="Symbol">(</a><a id="11958" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="11962" class="Symbol">(</a><a id="11963" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="11965" class="Symbol">_)</a> <a id="11968" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="11971" href="Category.Ambient.html#2115" class="Function">idC</a><a id="11974" class="Symbol">)</a> <a id="11976" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="11978" class="Symbol">(</a><a id="11979" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="11981" class="Symbol">(</a><a id="11982" href="Monad.Instance.K.Strong.html#10430" class="Bound">A</a> <a id="11984" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="11986" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="11990" href="Monad.Instance.K.Strong.html#10434" class="Bound">B</a><a id="11991" class="Symbol">)</a> <a id="11993" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="11996" href="Category.Ambient.html#2115" class="Function">idC</a><a id="11999" class="Symbol">)</a> <a id="12001" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12003" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="12017" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12019" class="Symbol">(</a><a id="12020" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="12024" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="12026" href="Monad.Instance.K.Strong.html#11398" class="Bound">h</a><a id="12027" class="Symbol">))</a> <a id="12030" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a> <a id="12032" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="12035" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="12044" class="Symbol">(</a><a id="12045" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="12054" class="Symbol">_)</a> <a id="12057" class="Symbol">(</a><a id="12058" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="12064" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a><a id="12069" class="Symbol">)</a> <a id="12071" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="12086" class="Symbol">((</a><a id="12088" href="Categories.NaturalTransformation.Core.html#783" class="Function">μ.η</a> <a id="12092" class="Symbol">_</a> <a id="12094" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12096" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="12100" class="Symbol">(</a><a id="12101" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="12103" class="Symbol">_)</a> <a id="12106" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="12109" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="12113" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12115" href="Category.Ambient.html#2115" class="Function">idC</a><a id="12118" class="Symbol">)</a> <a id="12120" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12122" class="Symbol">(</a><a id="12123" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="12125" class="Symbol">(</a><a id="12126" href="Monad.Instance.K.Strong.html#10430" class="Bound">A</a> <a id="12128" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="12130" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="12134" href="Monad.Instance.K.Strong.html#10434" class="Bound">B</a><a id="12135" class="Symbol">)</a> <a id="12137" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="12140" href="Category.Ambient.html#2115" class="Function">idC</a><a id="12143" class="Symbol">)</a> <a id="12145" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12147" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="12161" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="12163" class="Symbol">(</a><a id="12164" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="12168" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="12170" href="Monad.Instance.K.Strong.html#11398" class="Bound">h</a><a id="12171" class="Symbol">))</a> <a id="12174" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a>    <a id="12179" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="12182" href="Algebra.Elgot.html#2331" class="Function">#-resp-≈</a> <a id="12191" class="Symbol">(</a><a id="12192" href="Monad.Instance.K.html#1333" class="Function">algebras</a> <a id="12201" class="Symbol">_)</a> <a id="12204" class="Symbol">(</a><a id="12205" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="12211" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a><a id="12216" class="Symbol">)</a> <a id="12218" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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            <a id="15141" class="Symbol">(</a><a id="15142" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15144" class="Symbol">_</a> <a id="15146" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15148" class="Symbol">(</a><a id="15149" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15153" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15155" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15157" class="Symbol">_)</a> <a id="15160" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15162" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a><a id="15168" class="Symbol">)</a> <a id="15170" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15172" class="Symbol">(</a><a id="15173" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15177" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15179" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="15181" class="Symbol">_)</a>                                       <a id="15222" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="15225" class="Symbol">(</a><a id="15226" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="15234" href="Categories.Category.BinaryProducts.html#2599" class="Function">⁂∘⟨⟩</a><a id="15238" class="Symbol">)</a> <a id="15240" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="15248" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="15263" class="Symbol">(</a><a id="15264" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15266" class="Symbol">_</a> <a id="15268" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15270" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="15272" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15276" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15278" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15281" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15283" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15286" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="15288" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15290" class="Symbol">_</a> <a id="15292" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15294" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="15296" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="15299" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15301" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15304" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="15306" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="15309" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="15311" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="15312" class="Symbol">)</a> <a id="15314" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15316" class="Symbol">(</a><a id="15317" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15321" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15323" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="15325" class="Symbol">_)</a>                 <a id="15344" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="15347" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="15353" href="Categories.Category.BinaryProducts.html#2975" class="Function">⟨⟩∘</a> <a id="15357" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="15372" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15374" class="Symbol">_</a> <a id="15376" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15378" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="15380" class="Symbol">(</a><a id="15381" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15385" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15387" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15390" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15392" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="15394" class="Symbol">)</a> <a id="15396" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15398" class="Symbol">(</a><a id="15399" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15403" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15405" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="15407" class="Symbol">_)</a> <a id="15410" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="15412" class="Symbol">(</a><a id="15413" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15415" class="Symbol">_</a> <a id="15417" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15419" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="15421" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="15424" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15426" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15429" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="15431" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="15434" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="15435" class="Symbol">)</a> <a id="15437" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15439" class="Symbol">(</a><a id="15440" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15444" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15446" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="15448" class="Symbol">_)</a> <a id="15451" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="15453" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="15456" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="15464" class="Symbol">(</a><a id="15465" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="15474" class="Symbol">(</a><a id="15475" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="15485" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="15493" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="15495" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="15501" href="Categories.Category.BinaryProducts.html#2391" class="Function">π₁∘⁂</a><a id="15505" class="Symbol">)</a> <a id="15507" class="Symbol">(</a><a id="15508" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="15514" href="Categories.Category.BinaryProducts.html#2975" class="Function">⟨⟩∘</a><a id="15517" class="Symbol">))</a> <a id="15520" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="15535" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15537" class="Symbol">_</a> <a id="15539" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15541" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="15543" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15546" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15548" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15552" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15554" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15557" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="15559" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15561" class="Symbol">_</a> <a id="15563" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15565" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="15567" class="Symbol">(</a><a id="15568" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="15571" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15573" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="15575" class="Symbol">)</a> <a id="15577" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15579" class="Symbol">(</a><a id="15580" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15584" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15586" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="15588" class="Symbol">_)</a> <a id="15591" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="15593" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="15596" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15598" class="Symbol">(</a><a id="15599" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15603" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15605" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="15607" class="Symbol">_)</a> <a id="15610" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="15612" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a>   <a id="15616" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="15619" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="15627" class="Symbol">(</a><a id="15628" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="15637" class="Symbol">(</a><a id="15638" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="15646" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="15655" class="Symbol">)</a> <a id="15657" class="Symbol">(</a><a id="15658" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="15666" class="Symbol">(</a><a id="15667" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="15676" class="Symbol">(</a><a id="15677" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="15683" href="Categories.Category.BinaryProducts.html#2391" class="Function">π₁∘⁂</a><a id="15687" class="Symbol">)</a> <a id="15689" href="Categories.Category.BinaryProducts.html#2453" class="Function">π₂∘⁂</a><a id="15693" class="Symbol">)))</a> <a id="15697" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="15712" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15714" class="Symbol">_</a> <a id="15716" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15718" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="15720" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15723" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15725" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15728" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="15730" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15732" class="Symbol">_</a> <a id="15734" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15736" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="15738" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="15741" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15743" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15747" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15749" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15752" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="15754" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="15756" class="Symbol">_</a> <a id="15758" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15760" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="15763" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="15765" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a>                           <a id="15793" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="15796" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="15804" class="Symbol">(</a><a id="15805" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="15814" class="Symbol">(</a><a id="15815" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="15819" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="15828" class="Symbol">)</a> <a id="15830" class="Symbol">(</a><a id="15831" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="15839" class="Symbol">((</a><a id="15841" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="15850" class="Symbol">(</a><a id="15851" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="15855" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="15864" class="Symbol">)</a> <a id="15866" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="15870" class="Symbol">)</a> <a id="15872" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="15874" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="15878" href="Categories.Category.BinaryProducts.html#2599" class="Function">⁂∘⟨⟩</a><a id="15882" class="Symbol">)))</a> <a id="15886" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="15901" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15903" class="Symbol">_</a> <a id="15905" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15907" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="15909" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15913" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15915" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15918" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15920" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15923" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="15925" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="15927" class="Symbol">_</a> <a id="15929" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15931" class="Symbol">(</a><a id="15932" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15936" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="15938" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="15940" class="Symbol">_)</a> <a id="15943" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15945" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="15947" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="15950" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15952" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="15956" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="15958" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="15961" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="15963" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="15966" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="15968" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a>             <a id="15982" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="15985" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="15993" class="Symbol">(</a><a id="15994" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="16003" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="16008" class="Symbol">(</a><a id="16009" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="16015" class="Symbol">(</a><a id="16016" href="Monad.Instance.K.Strong.html#3312" class="Function">τ-η</a> <a id="16020" class="Symbol">(</a><a id="16021" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="16023" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="16025" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="16026" class="Symbol">))))</a> <a id="16031" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="16046" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16048" class="Symbol">_</a> <a id="16050" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16052" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="16054" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16058" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16060" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16063" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16065" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16068" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="16070" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="16072" class="Symbol">_</a> <a id="16074" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16076" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="16078" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="16081" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16083" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16087" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16089" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16092" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="16094" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="16097" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="16099" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a>                           <a id="16127" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="16130" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="16138" class="Symbol">(</a><a id="16139" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="16143" href="Categories.Category.BinaryProducts.html#2599" class="Function">⁂∘⟨⟩</a><a id="16147" class="Symbol">)</a> <a id="16149" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="16164" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16166" class="Symbol">_</a> <a id="16168" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16170" class="Symbol">(</a><a id="16171" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16175" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16177" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="16179" class="Symbol">_)</a> <a id="16182" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16184" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="16186" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16189" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16191" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16194" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="16196" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="16198" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="16201" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16203" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16207" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16209" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16212" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="16214" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="16217" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="16219" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a>                         <a id="16245" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="16248" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="16254" class="Symbol">(</a><a id="16255" href="Monad.Instance.K.Strong.html#3312" class="Function">τ-η</a> <a id="16259" class="Symbol">_)</a> <a id="16262" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="16277" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="16279" class="Symbol">_</a> <a id="16281" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16283" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="16285" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16288" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16290" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16293" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="16295" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="16297" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="16300" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16302" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16306" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16308" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16311" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="16313" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="16316" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="16318" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a>                                       <a id="16358" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="16361" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="16369" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="16378" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="16383" class="Symbol">(</a><a id="16384" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="16393" class="Symbol">(</a><a id="16394" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="16402" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="16411" class="Symbol">)</a> <a id="16413" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="16417" class="Symbol">)</a> <a id="16419" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="16434" href="Monad.Instance.K.Strong.html#2820" class="Function">η</a> <a id="16436" class="Symbol">(</a><a id="16437" href="Monad.Instance.K.Strong.html#14006" class="Bound">X</a> <a id="16439" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="16441" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="16443" href="Categories.Category.BinaryProducts.html#1053" class="Function Operator">×</a> <a id="16445" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="16446" class="Symbol">)</a> <a id="16448" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16450" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a>                                                           <a id="16515" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a><a id="16516" class="Symbol">)</a>
          <a id="16528" href="Monad.Instance.K.Strong.html#16528" class="Function">comm₃</a> <a id="16534" class="Symbol">:</a> <a id="16536" class="Symbol">∀</a> <a id="16538" class="Symbol">{</a><a id="16539" href="Monad.Instance.K.Strong.html#16539" class="Bound">A</a> <a id="16541" class="Symbol">:</a> <a id="16543" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="16546" class="Symbol">}</a> <a id="16548" class="Symbol">(</a><a id="16549" href="Monad.Instance.K.Strong.html#16549" class="Bound">h</a> <a id="16551" class="Symbol">:</a> <a id="16553" href="Monad.Instance.K.Strong.html#16539" class="Bound">A</a> <a id="16555" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="16557" href="Categories.Functor.Core.html#797" class="Function">K.₀</a> <a id="16561" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a> <a id="16563" href="Categories.Category.Cocartesian.html#1549" class="Function Operator">+</a> <a id="16565" href="Monad.Instance.K.Strong.html#16539" class="Bound">A</a><a id="16566" class="Symbol">)</a> <a id="16568" class="Symbol">→</a> <a id="16570" class="Symbol">(</a><a id="16571" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16573" class="Symbol">_</a> <a id="16575" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16577" class="Symbol">(</a><a id="16578" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16582" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16584" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16586" class="Symbol">_)</a> <a id="16589" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16591" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a><a id="16597" class="Symbol">)</a> <a id="16599" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16601" class="Symbol">(</a><a id="16602" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16606" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16608" href="Monad.Instance.K.Strong.html#16549" class="Bound">h</a> <a id="16610" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a><a id="16611" class="Symbol">)</a> <a id="16613" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="16615" class="Symbol">((</a><a id="16617" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16619" class="Symbol">_</a> <a id="16621" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16623" class="Symbol">(</a><a id="16624" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16628" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16630" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16632" class="Symbol">_)</a> <a id="16635" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16637" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a> <a id="16644" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="16647" href="Category.Ambient.html#2115" class="Function">idC</a><a id="16650" class="Symbol">)</a> <a id="16652" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16654" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="16668" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16670" class="Symbol">(</a><a id="16671" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16675" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16677" href="Monad.Instance.K.Strong.html#16549" class="Bound">h</a><a id="16678" class="Symbol">))</a> <a id="16681" href="Monad.Instance.K.Strong.html#2961
          <a id="16693" href="Monad.Instance.K.Strong.html#16528" class="Function">comm₃</a> <a id="16699" class="Symbol">{</a><a id="16700" href="Monad.Instance.K.Strong.html#16700" class="Bound">A</a><a id="16701" class="Symbol">}</a> <a id="16703" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a> <a id="16705" class="Symbol">=</a> <a id="16707" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a> 
            <a id="16726" class="Symbol">(</a><a id="16727" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16729" class="Symbol">_</a> <a id="16731" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16733" class="Symbol">(</a><a id="16734" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16738" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16740" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16742" class="Symbol">_)</a> <a id="16745" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16747" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a><a id="16753" class="Symbol">)</a> <a id="16755" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16757" class="Symbol">(</a><a id="16758" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16762" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16764" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a> <a id="16766" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a><a id="16767" class="Symbol">)</a>                                                         <a id="16825" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="16828" class="Symbol">(</a><a id="16829" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="16837" href="Categories.Category.BinaryProducts.html#2599" class="Function">⁂∘⟨⟩</a><a id="16841" class="Symbol">)</a> <a id="16843" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="16851" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="16866" class="Symbol">(</a><a id="16867" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16869" class="Symbol">_</a> <a id="16871" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16873" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="16875" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16879" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16881" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16884" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16886" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16889" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="16891" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16893" class="Symbol">_</a> <a id="16895" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16897" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="16899" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="16902" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16904" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="16907" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="16909" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="16912" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="16914" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="16915" class="Symbol">)</a> <a id="16917" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16919" class="Symbol">(</a><a id="16920" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="16924" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="16926" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a> <a id="16928" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a><a id="16929" class="Symbol">)</a>                                   <a id="16965" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="16968" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="16974" href="Categories.Category.BinaryProducts.html#2975" class="Function">⟨⟩∘</a> <a id="16978" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="16993" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="16995" class="Symbol">_</a> <a id="16997" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="16999" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="17001" class="Symbol">(</a><a id="17002" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="17006" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17008" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17011" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17013" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a><a id="17015" class="Symbol">)</a> <a id="17017" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17019" class="Symbol">(</a><a id="17020" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="17024" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="17026" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a> <a id="17028" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a><a id="17029" class="Symbol">)</a> <a id="17031" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="17033" class="Symbol">(</a><a id="17034" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="17036" class="Symbol">_</a> <a id="17038" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17040" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="17042" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="17045" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17047" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17050" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="17052" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="17055" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a><a id="17056" class="Symbol">)</a> <a id="17058" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17060" class="Symbol">(</a><a id="17061" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="17065" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="17067" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a> <a id="17069" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a><a id="17070" class="Symbol">)</a> <a id="17072" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a>                   <a id="17092" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="17095" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="17103" class="Symbol">(</a><a id="17104" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="17113" class="Symbol">(</a><a id="17114" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="17124" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="17132" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="17134" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="17140" href="Categories.Category.BinaryProducts.html#2391" class="Function">π₁∘⁂</a><a id="17144" class="Symbol">)</a> <a id="17146" class="Symbol">(</a><a id="17147" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="17153" href="Categories.Category.BinaryProducts.html#2975" class="Function">⟨⟩∘</a><a id="17156" class="Symbol">))</a> <a id="17159" href="Relation.Binary.Rea
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            <a id="17572" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="17574" class="Symbol">_</a> <a id="17576" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17578" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="17580" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17583" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17585" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17588" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="17590" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="17592" class="Symbol">_</a> <a id="17594" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17596" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="17598" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="17602" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17604" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="17607" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17609" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17612" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="17614" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a> <a id="17616" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a> <a id="17618" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17620" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="17623" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="17625" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a>                                             <a id="17671" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="17674" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="17682" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="17691" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="17696" class="Symbol">(</a><a id="17697" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="17705" class="Symbol">(</a><a id="17706" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="17710" href="Categories.Category.BinaryProducts.html#2599" class="Function">⁂∘⟨⟩</a><a id="17714" class="Symbol">))</a> <a id="17717" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="17732" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="17734" class="Symbol">_</a> <a id="17736" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17738" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="17740" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17743" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17745" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17748" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="17750" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="17752" class="Symbol">_</a> <a id="17754" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17756" class="Symbol">(</a><a id="17757" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="17761" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="17763" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a> <a id="17765" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a><a id="17766" class="Symbol">)</a> <a id="17768" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17770" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="17772" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="17775" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17777" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17780" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="17782" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="17785" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="17787" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a>                                           <a id="17831" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="17834" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="17842" class="Symbol">(</a><a id="17843" href="Categories.Object.Product.Core.html#854" class="Function">⟨⟩-cong₂</a> <a id="17852" class="Symbol">(</a><a id="17853" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="17857" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a><a id="17866" class="Symbol">)</a> <a id="17868" class="Symbol">(</a><a id="17869" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="17875" class="Symbol">(</a><a id="17876" href="Monad.Instance.K.Strong.html#5557" class="Function">τ-comm</a> <a id="17883" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="17884" class="Symbol">)))</a> <a id="17888" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
            <a id="17903" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="17905" class="Symbol">_</a> <a id="17907" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17909" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="17911" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="17915" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17917" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17920" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17922" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17925" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="17927" class="Symbol">(((</a><a id="17930" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="17932" class="Symbol">(</a><a id="17933" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="17935" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="17937" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="17938" class="Symbol">)</a> <a id="17940" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="17943" href="Category.Ambient.html#2115" class="Function">idC</a><a id="17946" class="Symbol">)</a> <a id="17948" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17950" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="17964" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17966" class="Symbol">(</a><a id="17967" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="17971" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="17973" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="17974" class="Symbol">))</a> <a id="17977" href="Monad.Instance.K.Strong.html#2961" class="Function Operator">#</a><a id="17978" class="Symbol">)</a> <a id="17980" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17982" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟨</a> <a id="17984" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="17987" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="17989" href="Categories.Object.Product.Core.html#526" class="Function">π₁</a> <a id="17992" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">,</a> <a id="17994" href="Categories.Object.Product.Core.html#546" class="Function">π₂</a> <a id="17997" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a> <a id="17999" href="Categories.Category.BinaryProducts.html#1396" class="Function Operator">⟩</a>  <a id="18002" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="18005" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="18013" class="Symbol">(</a><a id="18014" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="18018" href="Categories.Category.BinaryProducts.html#2599" class="Function">⁂∘⟨⟩</a><a id="18022" class="Symbol">)</a> <a id="18024" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
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                <a id="18715" class="Symbol">(</a><a id="18716" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="18720" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="18723" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a><a id="18729" class="Symbol">)</a> <a id="18731" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18733" class="Symbol">(</a><a id="18734" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="18736" class="Symbol">_</a> <a id="18738" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18740" class="Symbol">(</a><a id="18741" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="18745" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="18747" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="18749" class="Symbol">(</a><a id="18750" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="18752" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="18754" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="18755" class="Symbol">))</a> <a id="18758" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18760" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a> <a id="18767" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="18770" href="Category.Ambient.html#2115" class="Function">idC</a><a id="18773" class="Symbol">)</a> <a id="18775" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18777" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="18791" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18793" class="Symbol">(</a><a id="18794" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="18798" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="18800" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="18801" class="Symbol">)</a>                           <a id="18829" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="18832" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="18838" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="18844" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
                <a id="18863" class="Symbol">(</a><a id="18864" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="18868" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18870" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="18872" class="Symbol">_</a> <a id="18874" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18876" class="Symbol">(</a><a id="18877" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="18881" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="18883" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="18885" class="Symbol">(</a><a id="18886" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="18888" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="18890" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="18891" class="Symbol">))</a> <a id="18894" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18896" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a> <a id="18903" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="18906" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a> <a id="18913" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18915" href="Category.Ambient.html#2115" class="Function">idC</a><a id="18918" class="Symbol">)</a> <a id="18920" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18922" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="18936" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="18938" class="Symbol">(</a><a id="18939" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="18943" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="18945" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="18946" class="Symbol">)</a>                              <a id="18977" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="18980" class="Symbol">(</a><a id="18981" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="18990" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="19000" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a><a id="19007" class="Symbol">)</a> <a id="19009" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="19017" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
                <a id="19036" class="Symbol">(</a><a id="19037" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="19039" class="Symbol">_</a> <a id="19041" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19043" class="Symbol">(</a><a id="19044" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19048" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19050" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="19052" class="Symbol">(</a><a id="19053" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="19055" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="19057" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="19058" class="Symbol">))</a> <a id="19061" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19063" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a> <a id="19070" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19073" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19077" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19079" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a><a id="19085" class="Symbol">)</a> <a id="19087" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19089" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="19103" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19105" class="Symbol">(</a><a id="19106" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19110" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19112" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="19113" class="Symbol">)</a>                                    <a id="19150" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="19154" class="Symbol">(</a><a id="19155" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a> <a id="19161" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="19163" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="19172" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="19178" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="19182" class="Symbol">)</a> <a id="19184" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="19192" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a> 
                <a id="19211" class="Symbol">((</a><a id="19213" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="19215" class="Symbol">_</a> <a id="19217" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19219" class="Symbol">(</a><a id="19220" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19224" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19226" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="19228" class="Symbol">(</a><a id="19229" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="19231" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="19233" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="19234" class="Symbol">))</a> <a id="19237" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19240" href="Category.Ambient.html#2115" class="Function">idC</a><a id="19243" class="Symbol">)</a> <a id="19245" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19247" class="Symbol">(</a><a id="19248" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a> <a id="19255" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19258" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a><a id="19264" class="Symbol">))</a> <a id="19267" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19269" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="19283" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19285" class="Symbol">(</a><a id="19286" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19290" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19292" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="19293" class="Symbol">)</a>                               <a id="19325" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="19328" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="19334" class="Symbol">(</a><a id="19335" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="19341" class="Symbol">(</a><a id="19342" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="19346" href="Category.Ambient.html#4917" class="Function">distributeˡ⁻¹-assoc</a><a id="19365" class="Symbol">))</a> <a id="19368" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
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                <a id="19539" class="Symbol">(</a><a id="19540" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="19542" class="Symbol">_</a> <a id="19544" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19546" class="Symbol">(</a><a id="19547" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19551" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19553" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="19555" class="Symbol">_)</a> <a id="19558" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19561" href="Category.Ambient.html#2115" class="Function">idC</a><a id="19564" class="Symbol">)</a> <a id="19566" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19568" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="19582" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19584" class="Symbol">(</a><a id="19585" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19589" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19591" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="19604" class="Symbol">)</a> <a id="19606" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19608" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a> <a id="19615" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19617" class="Symbol">(</a><a id="19618" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19622" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19624" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="19625" class="Symbol">)</a>                           <a id="19653" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="19657" class="Symbol">(</a><a id="19658" href="Categories.Category.Cocartesian.html#2622" class="Function">+₁-cong₂</a> <a id="19667" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="19672" class="Symbol">(</a><a id="19673" href="Categories.Morphism.Reasoning.Core.html#2786" class="Function">elimʳ</a> <a id="19679" class="Symbol">(</a><a id="19680" href="Category.Ambient.html#2592" class="Function">⟨⟩-unique</a> <a id="19690" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a> <a id="19698" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a><a id="19705" class="Symbol">)))</a> <a id="19709" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="19717" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a> 
                <a id="19736" class="Symbol">(</a><a id="19737" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="19739" class="Symbol">_</a> <a id="19741" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19743" class="Symbol">(</a><a id="19744" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19748" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19750" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="19752" class="Symbol">_)</a> <a id="19755" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19758" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19762" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19764" class="Symbol">(</a><a id="19765" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19769" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19771" href="Category.Ambient.html#2115" class="Function">idC</a><a id="19774" class="Symbol">))</a> <a id="19777" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19779" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="19793" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19795" class="Symbol">(</a><a id="19796" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19800" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19802" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="19815" class="Symbol">)</a> <a id="19817" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19819" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a> <a id="19826" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19828" class="Symbol">(</a><a id="19829" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19833" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19835" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="19836" class="Symbol">)</a>             <a id="19850" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="19854" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="19860" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="19862" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="19868" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
                <a id="19886" class="Symbol">(((</a><a id="19889" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="19891" class="Symbol">_</a> <a id="19893" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19895" class="Symbol">(</a><a id="19896" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19900" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19902" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="19904" class="Symbol">_)</a> <a id="19907" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="19910" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19914" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19916" class="Symbol">(</a><a id="19917" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19921" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19923" href="Category.Ambient.html#2115" class="Function">idC</a><a id="19926" class="Symbol">))</a> <a id="19929" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19931" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="19944" class="Symbol">)</a> <a id="19946" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19948" class="Symbol">(</a><a id="19949" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19953" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19955" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="19968" class="Symbol">))</a> <a id="19971" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19973" href="Categories.Morphism.html#2023" class="Field">_≅_.to</a> <a id="19980" href="Categories.Category.BinaryProducts.html#1183" class="Function">×-assoc</a> <a id="19988" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="19990" class="Symbol">(</a><a id="19991" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="19995" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="19997" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="19998" class="Symbol">)</a> <a id="20000" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="20004" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="20010" class="Symbol">(</a><a id="20011" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="20017" class="Symbol">(</a><a id="20018" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="20024" href="Categories.Category.Cocartesian.html#2699" class="Function">+₁∘+₁</a><a id="20029" class="Symbol">))</a> <a id="20032" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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                <a id="20626" class="Symbol">(</a><a id="20627" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="20629" class="Symbol">_</a> <a id="20631" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="20634" href="Category.Ambient.html#2115" class="Function">idC</a><a id="20637" class="Symbol">)</a> <a id="20639" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20641" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="20655" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20657" class="Symbol">(</a><a id="20658" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="20662" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="20664" class="Symbol">(</a><a id="20665" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="20667" class="Symbol">(</a><a id="20668" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="20670" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="20672" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="20673" class="Symbol">)</a> <a id="20675" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="20678" href="Category.Ambient.html#2115" class="Function">idC</a><a id="20681" class="Symbol">)</a> <a id="20683" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20685" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="20698" class="Symbol">)</a> <a id="20700" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20702" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a> <a id="20709" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20711" class="Symbol">(</a><a id="20712" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="20716" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="20718" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="20719" class="Symbol">)</a>                    <a id="20740" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="20743" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="20751" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="20759" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="20767" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="20775" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="20783" class="Symbol">(</a><a id="20784" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="20788" class="Symbol">(</a><a id="20789" href="Category.Ambient.html#2592" class="Function">⟨⟩-unique</a> <a id="20799" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a> <a id="20807" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">id-comm</a><a id="20814" class="Symbol">))</a> <a id="20817" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="20822" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
                <a id="20841" class="Symbol">(</a><a id="20842" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="20844" class="Symbol">_</a> <a id="20846" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="20849" href="Category.Ambient.html#2115" class="Function">idC</a><a id="20852" class="Symbol">)</a> <a id="20854" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20856" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="20870" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20872" class="Symbol">(</a><a id="20873" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="20877" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="20879" class="Symbol">(</a><a id="20880" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="20882" class="Symbol">(</a><a id="20883" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="20885" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="20887" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="20888" class="Symbol">)</a> <a id="20890" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="20893" href="Category.Ambient.html#2115" class="Function">idC</a><a id="20896" class="Symbol">)</a> <a id="20898" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20900" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="20913" class="Symbol">)</a> <a id="20915" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20917" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a> <a id="20924" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="20926" class="Symbol">((</a><a id="20928" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="20932" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="20934" href="Category.Ambient.html#2115" class="Function">idC</a><a id="20937" class="Symbol">)</a> <a id="20939" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="20941" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="20942" class="Symbol">)</a>            <a id="20955" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="20958" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="20966" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="20974" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="20982" href="Categories.Category.BinaryProducts.html#6414" class="Function">assocˡ∘⁂</a> <a id="20991" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
                <a id="21010" class="Symbol">(</a><a id="21011" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21013" class="Symbol">_</a> <a id="21015" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21018" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21021" class="Symbol">)</a> <a id="21023" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21025" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="21039" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21041" class="Symbol">(</a><a id="21042" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21046" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21048" class="Symbol">(</a><a id="21049" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21051" class="Symbol">(</a><a id="21052" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="21054" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="21056" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="21057" class="Symbol">)</a> <a id="21059" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21062" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21065" class="Symbol">)</a> <a id="21067" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21069" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="21082" class="Symbol">)</a> <a id="21084" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21086" class="Symbol">(</a><a id="21087" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21091" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21093" class="Symbol">(</a><a id="21094" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21098" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21100" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="21101" class="Symbol">))</a> <a id="21104" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21106" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a>            <a id="21124" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="21128" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="21136" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="21144" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="21150" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
                <a id="21168" class="Symbol">(</a><a id="21169" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21171" class="Symbol">_</a> <a id="21173" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21176" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21179" class="Symbol">)</a> <a id="21181" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21183" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="21197" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21199" class="Symbol">((</a><a id="21201" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21205" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21207" class="Symbol">(</a><a id="21208" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21210" class="Symbol">(</a><a id="21211" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="21213" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="21215" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="21216" class="Symbol">)</a> <a id="21218" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21221" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21224" class="Symbol">)</a> <a id="21226" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21228" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="21241" class="Symbol">)</a> <a id="21243" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21245" class="Symbol">(</a><a id="21246" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21250" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21252" class="Symbol">(</a><a id="21253" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21257" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21259" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="21260" class="Symbol">)))</a> <a id="21264" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21266" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a>          <a id="21282" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="21285" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="21293" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="21301" href="Categories.Category.BinaryProducts.html#2881" class="Function">⁂∘⁂</a> <a id="21305" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="21313" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
                <a id="21332" class="Symbol">(</a><a id="21333" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21335" class="Symbol">_</a> <a id="21337" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21340" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21343" class="Symbol">)</a> <a id="21345" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21347" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="21361" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21363" class="Symbol">(</a><a id="21364" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21368" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21370" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21374" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21376" class="Symbol">((</a><a id="21378" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21380" class="Symbol">(</a><a id="21381" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="21383" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="21385" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="21386" class="Symbol">)</a> <a id="21388" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21391" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21394" class="Symbol">)</a> <a id="21396" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21398" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a><a id="21411" class="Symbol">)</a> <a id="21413" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21415" class="Symbol">(</a><a id="21416" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21420" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21422" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="21423" class="Symbol">))</a> <a id="21426" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21428" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a>            <a id="21446" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="21449" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="21457" class="Symbol">(</a><a id="21458" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="21466" class="Symbol">((</a><a id="21468" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="21476" href="Categories.Category.Core.html#1339" class="Function">identity²</a> <a id="21486" href="Categories.Category.Core.html#715" class="Function">assoc</a><a id="21491" class="Symbol">)</a> <a id="21493" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a><a id="21500" class="Symbol">)</a> <a id="21502" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="21504" href="Categories.Category.Core.html#1004" class="Function">sym-assoc</a><a id="21513" class="Symbol">)</a> <a id="21515" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="21517" href="Categories.Category.Core.html#1004" class="Function">sym-assoc</a> <a id="21527" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
                <a id="21545" class="Symbol">((</a><a id="21547" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21549" class="Symbol">_</a> <a id="21551" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21554" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21557" class="Symbol">)</a> <a id="21559" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21561" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="21575" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21577" class="Symbol">(</a><a id="21578" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21582" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21584" class="Symbol">(</a><a id="21585" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21587" class="Symbol">(</a><a id="21588" href="Monad.Instance.K.Strong.html#14010" class="Bound">Y</a> <a id="21590" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="21592" href="Monad.Instance.K.Strong.html#14014" class="Bound">Z</a><a id="21593" class="Symbol">)</a> <a id="21595" href="Categories.Category.Cocartesian.html#2133" class="Function Operator">+₁</a> <a id="21598" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21601" class="Symbol">)</a> <a id="21603" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21605" href="Categories.Category.Distributive.html#3168" class="Function">distributeˡ⁻¹</a> <a id="21619" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21621" class="Symbol">(</a><a id="21622" href="Category.Ambient.html#2115" class="Function">idC</a> <a id="21626" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21628" href="Monad.Instance.K.Strong.html#16703" class="Bound">h</a><a id="21629" class="Symbol">)))</a> <a id="21633" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21635" href="Categories.Category.BinaryProducts.html#1542" class="Function">assocˡ</a>                  <a id="21659" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>

  <a id="KStrong"></a><a id="21664" href="Monad.Instance.K.Strong.html#21664" class="Function">KStrong</a> <a id="21672" class="Symbol">:</a> <a id="21674" href="Categories.Monad.Strong.html#1832" class="Record">StrongMonad</a> <a id="21686" class="Symbol">{</a><a id="21687" class="Argument">C</a> <a id="21689" class="Symbol">=</a> <a id="21691" href="Category.Ambient.html#1757" class="Function">C</a><a id="21692" class="Symbol">}</a> <a id="21694" href="Category.Ambient.html#2297" class="Function">monoidal</a>
  <a id="21705" href="Monad.Instance.K.Strong.html#21664" class="Function">KStrong</a> <a id="21713" class="Symbol">=</a> <a id="21715" class="Keyword">record</a> 
    <a id="21727" class="Symbol">{</a> <a id="21729" href="Categories.Monad.Strong.html#1918" class="Field">M</a> <a id="21731" class="Symbol">=</a> <a id="21733" href="Monad.Instance.K.html#1609" class="Function">monadK</a>
    <a id="21744" class="Symbol">;</a> <a id="21746" href="Categories.Monad.Strong.html#1941" class="Field">strength</a> <a id="21755" class="Symbol">=</a> <a id="21757" href="Monad.Instance.K.Strong.html#5973" class="Function">KStrength</a>
    <a id="21771" class="Symbol">}</a>

  <a id="τ-comm-id"></a><a id="21776" href="Monad.Instance.K.Strong.html#21776" class="Function">τ-comm-id</a> <a id="21786" class="Symbol">:</a> <a id="21788" class="Symbol">∀</a> <a id="21790" class="Symbol">{</a><a id="21791" href="Monad.Instance.K.Strong.html#21791" class="Bound">X</a> <a id="21793" href="Monad.Instance.K.Strong.html#21793" class="Bound">Y</a> <a id="21795" href="Monad.Instance.K.Strong.html#21795" class="Bound">Z</a><a id="21796" class="Symbol">}</a> <a id="21798" class="Symbol">(</a><a id="21799" href="Monad.Instance.K.Strong.html#21799" class="Bound">f</a> <a id="21801" class="Symbol">:</a> <a id="21803" href="Monad.Instance.K.Strong.html#21791" class="Bound">X</a> <a id="21805" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="21807" href="Monad.Instance.K.Strong.html#21793" class="Bound">Y</a><a id="21808" class="Symbol">)</a> <a id="21810" class="Symbol">→</a> <a id="21812" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21814" class="Symbol">(</a><a id="21815" href="Monad.Instance.K.Strong.html#21793" class="Bound">Y</a> <a id="21817" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="21819" href="Monad.Instance.K.Strong.html#21795" class="Bound">Z</a><a id="21820" class="Symbol">)</a> <a id="21822" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21824" class="Symbol">(</a><a id="21825" href="Monad.Instance.K.Strong.html#21799" class="Bound">f</a> <a id="21827" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21829" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21832" class="Symbol">)</a> <a id="21834" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="21836" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="21840" class="Symbol">(</a><a id="21841" href="Monad.Instance.K.Strong.html#21799" class="Bound">f</a> <a id="21843" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21845" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21848" class="Symbol">)</a> <a id="21850" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21852" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21854" class="Symbol">(</a><a id="21855" href="Monad.Instance.K.Strong.html#21791" class="Bound">X</a> <a id="21857" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="21859" href="Monad.Instance.K.Strong.html#21795" class="Bound">Z</a><a id="21860" class="Symbol">)</a>
  <a id="21864" href="Monad.Instance.K.Strong.html#21776" class="Function">τ-comm-id</a> <a id="21874" class="Symbol">{</a><a id="21875" href="Monad.Instance.K.Strong.html#21875" class="Bound">X</a><a id="21876" class="Symbol">}</a> <a id="21878" class="Symbol">{</a><a id="21879" href="Monad.Instance.K.Strong.html#21879" class="Bound">Y</a><a id="21880" class="Symbol">}</a> <a id="21882" class="Symbol">{</a><a id="21883" href="Monad.Instance.K.Strong.html#21883" class="Bound">Z</a><a id="21884" class="Symbol">}</a> <a id="21886" href="Monad.Instance.K.Strong.html#21886" class="Bound">f</a> <a id="21888" class="Symbol">=</a> <a id="21890" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a> 
    <a id="21901" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21903" class="Symbol">(</a><a id="21904" href="Monad.Instance.K.Strong.html#21879" class="Bound">Y</a> <a id="21906" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="21908" href="Monad.Instance.K.Strong.html#21883" class="Bound">Z</a><a id="21909" class="Symbol">)</a> <a id="21911" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21913" class="Symbol">(</a><a id="21914" href="Monad.Instance.K.Strong.html#21886" class="Bound">f</a> <a id="21916" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21918" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21921" class="Symbol">)</a> <a id="21923" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="21926" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="21934" class="Symbol">(</a><a id="21935" href="Categories.Category.BinaryProducts.html#2515" class="Function">⁂-cong₂</a> <a id="21943" href="Relation.Binary.Structures.html#1596" class="Function">refl</a> <a id="21948" class="Symbol">(</a><a id="21949" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="21953" href="Categories.Functor.Core.html#511" class="Function">K.identity</a><a id="21963" class="Symbol">))</a> <a id="21966" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
    <a id="21973" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="21975" class="Symbol">(</a><a id="21976" href="Monad.Instance.K.Strong.html#21879" class="Bound">Y</a> <a id="21978" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="21980" href="Monad.Instance.K.Strong.html#21883" class="Bound">Z</a><a id="21981" class="Symbol">)</a> <a id="21983" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="21985" class="Symbol">(</a><a id="21986" href="Monad.Instance.K.Strong.html#21886" class="Bound">f</a> <a id="21988" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="21990" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="21994" href="Category.Ambient.html#2115" class="Function">idC</a><a id="21997" class="Symbol">)</a> <a id="21999" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="22002" href="Categories.NaturalTransformation.Core.html#827" class="Function">strengthen.commute</a> <a id="22021" class="Symbol">(</a><a id="22022" href="Monad.Instance.K.Strong.html#21886" class="Bound">f</a> <a id="22024" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="22026" href="Category.Ambient.html#2115" class="Function">idC</a><a id="22029" class="Symbol">)</a> <a id="22031" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a> 
    <a id="22038" href="Categories.Functor.Core.html#806" class="Function">K.₁</a> <a id="22042" class="Symbol">(</a><a id="22043" href="Monad.Instance.K.Strong.html#21886" class="Bound">f</a> <a id="22045" href="Categories.Category.BinaryProducts.html#1465" class="Function Operator">⁂</a> <a id="22047" href="Category.Ambient.html#2115" class="Function">idC</a><a id="22050" class="Symbol">)</a> <a id="22052" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="22054" href="Monad.Instance.K.Strong.html#3259" class="Function">τ</a> <a id="22056" class="Symbol">(</a><a id="22057" href="Monad.Instance.K.Strong.html#21875" class="Bound">X</a> <a id="22059" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="22061" href="Monad.Instance.K.Strong.html#21883" class="Bound">Z</a><a id="22062" class="Symbol">)</a> <a id="22064" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
    <a id="22070" class="Keyword">where</a>
      <a id="22082" class="Keyword">open</a> <a id="22087" href="Categories.Monad.Strong.html#764" class="Module">Strength</a> <a id="22096" href="Monad.Instance.K.Strong.html#5973" class="Function">KStrength</a> <a id="22106" class="Keyword">using</a> <a id="22112" class="Symbol">(</a><a id="22113" href="Categories.Monad.Strong.html#1060" class="Field">strengthen</a><a id="22123" class="Symbol">)</a>

  <a id="22128" class="Keyword">module</a> <a id="strongK"></a><a id="22135" href="Monad.Instance.K.Strong.html#22135" class="Module">strongK</a> <a id="22143" class="Symbol">=</a> <a id="22145" href="Categories.Monad.Strong.html#1832" class="Module">StrongMonad</a> <a id="22157" href="Monad.Instance.K.Strong.html#21664" class="Function">KStrong</a>
</pre>