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271 lines
130 KiB
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<html><head><meta charset="utf-8"><title>Categories.Category.Monoidal.Properties</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Symbol">{-#</a> <a id="5" class="Keyword">OPTIONS</a> <a id="13" class="Pragma">--without-K</a> <a id="25" class="Pragma">--safe</a> <a id="32" class="Symbol">#-}</a>
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<a id="36" class="Keyword">open</a> <a id="41" class="Keyword">import</a> <a id="48" href="Categories.Category.html" class="Module">Categories.Category</a>
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<a id="68" class="Keyword">import</a> <a id="75" href="Categories.Category.Monoidal.html" class="Module">Categories.Category.Monoidal</a> <a id="104" class="Symbol">as</a> <a id="107" class="Module">M</a>
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<a id="110" class="Comment">-- Properties of Monoidal Categories</a>
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<a id="148" class="Keyword">module</a> <a id="155" href="Categories.Category.Monoidal.Properties.html" class="Module">Categories.Category.Monoidal.Properties</a>
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<a id="197" class="Symbol">{</a><a id="198" href="Categories.Category.Monoidal.Properties.html#198" class="Bound">o</a> <a id="200" href="Categories.Category.Monoidal.Properties.html#200" class="Bound">ℓ</a> <a id="202" href="Categories.Category.Monoidal.Properties.html#202" class="Bound">e</a><a id="203" class="Symbol">}</a> <a id="205" class="Symbol">{</a><a id="206" href="Categories.Category.Monoidal.Properties.html#206" class="Bound">C</a> <a id="208" class="Symbol">:</a> <a id="210" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="219" href="Categories.Category.Monoidal.Properties.html#198" class="Bound">o</a> <a id="221" href="Categories.Category.Monoidal.Properties.html#200" class="Bound">ℓ</a> <a id="223" href="Categories.Category.Monoidal.Properties.html#202" class="Bound">e</a><a id="224" class="Symbol">}</a> <a id="226" class="Symbol">(</a><a id="227" href="Categories.Category.Monoidal.Properties.html#227" class="Bound">MC</a> <a id="230" class="Symbol">:</a> <a id="232" href="Categories.Category.Monoidal.Core.html#1287" class="Record">M.Monoidal</a> <a id="243" href="Categories.Category.Monoidal.Properties.html#206" class="Bound">C</a><a id="244" class="Symbol">)</a> <a id="246" class="Keyword">where</a>
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<a id="253" class="Keyword">open</a> <a id="258" class="Keyword">import</a> <a id="265" href="Data.Product.html" class="Module">Data.Product</a> <a id="278" class="Keyword">using</a> <a id="284" class="Symbol">(</a><a id="285" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">_,_</a><a id="288" class="Symbol">;</a> <a id="290" href="Agda.Builtin.Sigma.html#165" class="Record">Σ</a><a id="291" class="Symbol">;</a> <a id="293" href="Data.Product.Base.html#4571" class="Function">uncurry′</a><a id="301" class="Symbol">)</a>
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<a id="304" class="Keyword">open</a> <a id="309" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="318" href="Categories.Category.Monoidal.Properties.html#206" class="Bound">C</a>
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<a id="320" class="Keyword">open</a> <a id="325" href="Categories.Category.Monoidal.Core.html#1287" class="Module">M.Monoidal</a> <a id="336" href="Categories.Category.Monoidal.Properties.html#227" class="Bound">MC</a>
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<a id="339" class="Keyword">open</a> <a id="344" class="Keyword">import</a> <a id="351" href="Categories.Category.Monoidal.Utilities.html" class="Module">Categories.Category.Monoidal.Utilities</a> <a id="390" href="Categories.Category.Monoidal.Properties.html#227" class="Bound">MC</a>
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<a id="393" class="Keyword">import</a> <a id="400" href="Categories.Category.Monoidal.Reasoning.html" class="Module">Categories.Category.Monoidal.Reasoning</a> <a id="439" class="Symbol">as</a> <a id="442" class="Module">MonR</a>
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<a id="447" class="Keyword">open</a> <a id="452" class="Keyword">import</a> <a id="459" href="Categories.Category.Construction.Core.html" class="Module">Categories.Category.Construction.Core</a> <a id="497" href="Categories.Category.Monoidal.Properties.html#206" class="Bound">C</a> as <a id="Core"></a><a id="502" href="Categories.Category.Monoidal.Properties.html#502" class="Module">Core</a> <a id="507" class="Keyword">using</a> <a id="513" class="Symbol">(</a><a id="514" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a><a id="518" class="Symbol">)</a>
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<a id="520" class="Keyword">open</a> <a id="525" class="Keyword">import</a> <a id="532" href="Categories.Category.Product.html" class="Module">Categories.Category.Product</a> <a id="560" class="Keyword">using</a> <a id="566" class="Symbol">(</a><a id="567" href="Categories.Category.Product.html#745" class="Function">Product</a><a id="574" class="Symbol">)</a>
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<a id="576" class="Keyword">open</a> <a id="581" class="Keyword">import</a> <a id="588" href="Categories.Functor.html" class="Module">Categories.Functor</a> <a id="607" class="Keyword">using</a> <a id="613" class="Symbol">(</a><a id="614" href="Categories.Functor.Core.html#248" class="Record">Functor</a><a id="621" class="Symbol">)</a>
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<a id="623" class="Keyword">open</a> <a id="628" class="Keyword">import</a> <a id="635" href="Categories.Functor.Bifunctor.html" class="Module">Categories.Functor.Bifunctor</a>
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<a id="664" class="Keyword">open</a> <a id="669" class="Keyword">import</a> <a id="676" href="Categories.Functor.Properties.html" class="Module">Categories.Functor.Properties</a>
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<a id="706" class="Keyword">open</a> <a id="711" class="Keyword">import</a> <a id="718" href="Categories.Morphism.Isomorphism.html" class="Module">Categories.Morphism.Isomorphism</a> <a id="750" href="Categories.Category.Monoidal.Properties.html#206" class="Bound">C</a>
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<a id="754" class="Keyword">using</a> <a id="760" class="Symbol">(</a><a id="761" href="Categories.Morphism.Isomorphism.html#8476" class="Function">elim-triangleˡ′</a><a id="776" class="Symbol">;</a> <a id="778" href="Categories.Morphism.Isomorphism.html#7806" class="Function">triangle-prism</a><a id="792" class="Symbol">;</a> <a id="794" href="Categories.Morphism.Isomorphism.html#8812" class="Function">cut-squareʳ</a><a id="805" class="Symbol">)</a>
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<a id="807" class="Keyword">import</a> <a id="814" href="Categories.Morphism.Reasoning.html" class="Module">Categories.Morphism.Reasoning</a> <a id="844" class="Symbol">as</a> <a id="847" class="Module">MR</a>
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<a id="850" class="Keyword">open</a> <a id="855" class="Keyword">import</a> <a id="862" href="Categories.NaturalTransformation.NaturalIsomorphism.Properties.html" class="Module">Categories.NaturalTransformation.NaturalIsomorphism.Properties</a>
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<a id="927" class="Keyword">using</a> <a id="933" class="Symbol">(</a><a id="934" href="Categories.NaturalTransformation.NaturalIsomorphism.Properties.html#1621" class="Function">push-eq</a><a id="941" class="Symbol">)</a>
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<a id="944" class="Keyword">private</a>
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<a id="954" class="Keyword">module</a> <a id="C"></a><a id="961" href="Categories.Category.Monoidal.Properties.html#961" class="Module">C</a> <a id="963" class="Symbol">=</a> <a id="965" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="974" href="Categories.Category.Monoidal.Properties.html#206" class="Bound">C</a>
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<a id="978" class="Keyword">variable</a>
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<a id="991" href="Categories.Category.Monoidal.Properties.html#991" class="Generalizable">A</a> <a id="993" href="Categories.Category.Monoidal.Properties.html#993" class="Generalizable">B</a> <a id="995" class="Symbol">:</a> <a id="997" href="Categories.Category.Core.html#559" class="Function">Obj</a>
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<a id="1001" class="Keyword">open</a> <a id="1006" href="Categories.Category.Construction.Core.html#1314" class="Module">Core.Shorthands</a>
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<a id="⊗-iso"></a><a id="1023" href="Categories.Category.Monoidal.Properties.html#1023" class="Function">⊗-iso</a> <a id="1029" class="Symbol">:</a> <a id="1031" href="Categories.Functor.Bifunctor.html#441" class="Function">Bifunctor</a> <a id="1041" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a> <a id="1046" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a> <a id="1051" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a>
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<a id="1056" href="Categories.Category.Monoidal.Properties.html#1023" class="Function">⊗-iso</a> <a id="1062" class="Symbol">=</a> <a id="1064" class="Keyword">record</a>
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<a id="1073" class="Symbol">{</a> <a id="1075" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="1088" class="Symbol">=</a> <a id="1090" href="Data.Product.Base.html#4571" class="Function">uncurry′</a> <a id="1099" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">_⊗₀_</a>
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<a id="1106" class="Symbol">;</a> <a id="1108" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="1121" class="Symbol">=</a> <a id="1124" class="Symbol">λ</a> <a id="1126" class="Keyword">where</a> <a id="1132" class="Symbol">(</a><a id="1133" href="Categories.Category.Monoidal.Properties.html#1133" class="Bound">f</a> <a id="1135" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1137" href="Categories.Category.Monoidal.Properties.html#1137" class="Bound">g</a><a id="1138" class="Symbol">)</a> <a id="1140" class="Symbol">→</a> <a id="1142" href="Categories.Category.Monoidal.Properties.html#1133" class="Bound">f</a> <a id="1144" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="1147" href="Categories.Category.Monoidal.Properties.html#1137" class="Bound">g</a>
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<a id="1151" class="Symbol">;</a> <a id="1153" href="Categories.Functor.Core.html#511" class="Field">identity</a> <a id="1166" class="Symbol">=</a> <a id="1168" href="Categories.Category.Monoidal.Utilities.html#4325" class="Function">refl⊗refl≃refl</a>
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<a id="1185" class="Symbol">;</a> <a id="1187" href="Categories.Functor.Core.html#565" class="Field">homomorphism</a> <a id="1200" class="Symbol">=</a> <a id="1202" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="1204" href="Categories.Functor.Core.html#565" class="Function">homomorphism</a> <a id="1217" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
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<a id="1221" class="Symbol">;</a> <a id="1223" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a> <a id="1236" class="Symbol">=</a> <a id="1238" class="Symbol">λ</a> <a id="1240" class="Keyword">where</a> <a id="1246" class="Symbol">(</a><a id="1247" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="1249" href="Categories.Category.Monoidal.Properties.html#1249" class="Bound">eq₁</a> <a id="1253" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a> <a id="1255" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1257" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="1259" href="Categories.Category.Monoidal.Properties.html#1259" class="Bound">eq₂</a> <a id="1263" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a><a id="1264" class="Symbol">)</a> <a id="1266" class="Symbol">→</a> <a id="1268" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="1270" href="Categories.Functor.Core.html#696" class="Function">F-resp-≈</a> <a id="1279" class="Symbol">(</a><a id="1280" href="Categories.Category.Monoidal.Properties.html#1249" class="Bound">eq₁</a> <a id="1284" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1286" href="Categories.Category.Monoidal.Properties.html#1259" class="Bound">eq₂</a><a id="1289" class="Symbol">)</a> <a id="1291" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
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<a id="1295" class="Symbol">}</a>
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<a id="1299" class="Keyword">where</a> <a id="1305" class="Keyword">open</a> <a id="1310" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="1318" href="Categories.Category.Monoidal.Core.html#1355" class="Field">⊗</a>
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<a id="_⊗ᵢ-"></a><a id="1321" href="Categories.Category.Monoidal.Properties.html#1321" class="Function Operator">_⊗ᵢ-</a> <a id="1326" class="Symbol">:</a> <a id="1328" href="Categories.Category.Core.html#559" class="Function">Obj</a> <a id="1332" class="Symbol">→</a> <a id="1334" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1342" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a> <a id="1347" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a>
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<a id="1352" href="Categories.Category.Monoidal.Properties.html#1352" class="Bound">X</a> <a id="1354" href="Categories.Category.Monoidal.Properties.html#1321" class="Function Operator">⊗ᵢ-</a> <a id="1358" class="Symbol">=</a> <a id="1360" href="Categories.Functor.Bifunctor.html#874" class="Function">appˡ</a> <a id="1365" href="Categories.Category.Monoidal.Properties.html#1023" class="Function">⊗-iso</a> <a id="1371" href="Categories.Category.Monoidal.Properties.html#1352" class="Bound">X</a>
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<a id="-⊗ᵢ_"></a><a id="1374" href="Categories.Category.Monoidal.Properties.html#1374" class="Function Operator">-⊗ᵢ_</a> <a id="1379" class="Symbol">:</a> <a id="1381" href="Categories.Category.Core.html#559" class="Function">Obj</a> <a id="1385" class="Symbol">→</a> <a id="1387" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1395" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a> <a id="1400" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a>
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<a id="1405" href="Categories.Category.Monoidal.Properties.html#1374" class="Function Operator">-⊗ᵢ</a> <a id="1409" href="Categories.Category.Monoidal.Properties.html#1409" class="Bound">X</a> <a id="1411" class="Symbol">=</a> <a id="1413" href="Categories.Functor.Bifunctor.html#938" class="Function">appʳ</a> <a id="1418" href="Categories.Category.Monoidal.Properties.html#1023" class="Function">⊗-iso</a> <a id="1424" href="Categories.Category.Monoidal.Properties.html#1409" class="Bound">X</a>
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<a id="1427" class="Comment">-- Coherence laws due to Mac Lane (1963) that were subsequently proven</a>
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<a id="1498" class="Comment">-- admissible by Max Kelly (1964). See</a>
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<a id="1538" class="Comment">-- https://ncatlab.org/nlab/show/monoidal+category#other_coherence_conditions</a>
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<a id="1616" class="Comment">-- for more details.</a>
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<a id="1638" class="Keyword">module</a> <a id="Kelly's"></a><a id="1645" href="Categories.Category.Monoidal.Properties.html#1645" class="Module">Kelly's</a> <a id="1653" class="Keyword">where</a>
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<a id="1661" class="Keyword">open</a> <a id="1666" href="Categories.Functor.Core.html#248" class="Module">Functor</a>
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<a id="1676" class="Keyword">open</a> <a id="1681" href="Categories.Category.Monoidal.Utilities.html#1438" class="Module">Shorthands</a>
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<a id="1694" class="Keyword">open</a> <a id="1699" href="Categories.Category.html#1298" class="Module">Commutation</a> <a id="1711" href="Categories.Category.Monoidal.Properties.html#206" class="Bound">C</a>
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<a id="1715" class="Keyword">open</a> <a id="1720" href="Categories.Category.Construction.Core.html#1340" class="Module">Commutationᵢ</a>
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<a id="1736" class="Keyword">private</a>
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<a id="1748" class="Keyword">variable</a>
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<a id="1763" href="Categories.Category.Monoidal.Properties.html#1763" class="Generalizable">f</a> <a id="1765" href="Categories.Category.Monoidal.Properties.html#1765" class="Generalizable">f′</a> <a id="1768" href="Categories.Category.Monoidal.Properties.html#1768" class="Generalizable">g</a> <a id="1770" href="Categories.Category.Monoidal.Properties.html#1770" class="Generalizable">h</a> <a id="1772" href="Categories.Category.Monoidal.Properties.html#1772" class="Generalizable">h′</a> <a id="1775" href="Categories.Category.Monoidal.Properties.html#1775" class="Generalizable">i</a> <a id="1777" href="Categories.Category.Monoidal.Properties.html#1777" class="Generalizable">i′</a> <a id="1780" href="Categories.Category.Monoidal.Properties.html#1780" class="Generalizable">j</a> <a id="1782" href="Categories.Category.Monoidal.Properties.html#1782" class="Generalizable">k</a> <a id="1784" class="Symbol">:</a> <a id="1786" href="Categories.Category.Monoidal.Properties.html#991" class="Generalizable">A</a> <a id="1788" href="Categories.Category.Core.html#575" class="Function Operator">≅</a> <a id="1790" href="Categories.Category.Monoidal.Properties.html#993" class="Generalizable">B</a>
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<a id="1795" class="Keyword">module</a> <a id="1802" href="Categories.Category.Monoidal.Properties.html#1802" class="Module">_</a> <a id="1804" class="Symbol">{</a><a id="1805" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="1807" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="1809" class="Symbol">:</a> <a id="1811" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="1814" class="Symbol">}</a> <a id="1816" class="Keyword">where</a>
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<a id="1826" class="Keyword">open</a> <a id="1831" href="Categories.Category.Core.html#2462" class="Module">HomReasoningᵢ</a>
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<a id="1850" class="Comment">-- TS: following three isos commute</a>
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<a id="1891" href="Categories.Category.Monoidal.Properties.html#1891" class="Function">ua</a> <a id="1894" class="Symbol">:</a> <a id="1896" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="1901" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="1904" class="Symbol">(</a><a id="1905" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="1910" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="1913" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="1914" class="Symbol">)</a> <a id="1916" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="1919" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="1921" href="Categories.Category.Core.html#575" class="Function Operator">≅</a> <a id="1923" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="1928" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="1931" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="1936" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="1939" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="1941" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="1944" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a>
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<a id="1950" href="Categories.Category.Monoidal.Properties.html#1891" class="Function">ua</a> <a id="1953" class="Symbol">=</a> <a id="1955" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="1959" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="1962" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a>
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<a id="1978" href="Categories.Category.Monoidal.Properties.html#1978" class="Function">u[λY]</a> <a id="1984" class="Symbol">:</a> <a id="1986" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="1991" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="1994" class="Symbol">(</a><a id="1995" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2000" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2003" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="2004" class="Symbol">)</a> <a id="2006" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2009" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="2011" href="Categories.Category.Core.html#575" class="Function Operator">≅</a> <a id="2013" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2018" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2021" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="2023" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2026" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a>
|
|||
|
|
<a id="2032" href="Categories.Category.Monoidal.Properties.html#1978" class="Function">u[λY]</a> <a id="2038" class="Symbol">=</a> <a id="2040" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="2044" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="2047" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="2055" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="2058" href="Categories.Category.Core.html#630" class="Function">idᵢ</a>
|
|||
|
|
|
|||
|
|
<a id="2067" href="Categories.Category.Monoidal.Properties.html#2067" class="Function">uλ</a> <a id="2070" class="Symbol">:</a> <a id="2072" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2077" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2080" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2085" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2088" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="2090" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2093" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="2095" href="Categories.Category.Core.html#575" class="Function Operator">≅</a> <a id="2097" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2102" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2105" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="2107" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2110" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a>
|
|||
|
|
<a id="2116" href="Categories.Category.Monoidal.Properties.html#2067" class="Function">uλ</a> <a id="2119" class="Symbol">=</a> <a id="2121" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="2125" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="2128" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a>
|
|||
|
|
|
|||
|
|
<a id="2141" class="Comment">-- setups</a>
|
|||
|
|
|
|||
|
|
<a id="2156" href="Categories.Category.Monoidal.Properties.html#2156" class="Function">perimeter</a> <a id="2166" class="Symbol">:</a> <a id="2168" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="2170" class="Symbol">((</a><a id="2172" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2177" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2180" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="2184" class="Symbol">)</a> <a id="2186" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2189" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="2190" class="Symbol">)</a> <a id="2192" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2195" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="2197" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="2199" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2204" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2207" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="2209" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2212" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="2214" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="2235" class="Symbol">(</a><a id="2236" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="2244" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="2247" href="Categories.Category.Core.html#630" class="Function">idᵢ</a><a id="2250" class="Symbol">)</a> <a id="2252" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="2255" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="2262" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="2265" class="Symbol">(</a><a id="2266" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2271" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2274" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="2275" class="Symbol">)</a> <a id="2277" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2280" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="2282" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="2302" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a>
|
|||
|
|
<a id="2329" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="2331" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="2358" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="2361" class="Symbol">(</a><a id="2362" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2367" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2370" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="2374" class="Symbol">)</a> <a id="2376" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2379" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="2381" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2384" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="2386" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="2406" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="2433" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="2436" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2441" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2444" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2449" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2452" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="2454" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2457" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="2459" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="2479" href="Categories.Category.Monoidal.Properties.html#2067" class="Function">uλ</a>
|
|||
|
|
<a id="2498" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="2504" href="Categories.Category.Monoidal.Properties.html#2156" class="Function">perimeter</a> <a id="2514" class="Symbol">=</a> <a id="2516" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="2518" class="Symbol">(</a><a id="2519" href="Categories.Morphism.Reasoning.Core.html#5295" class="Function">glue◃◽′</a> <a id="2527" href="Categories.Category.Monoidal.Utilities.html#3894" class="Function">triangle-iso</a>
|
|||
|
|
<a id="2569" class="Symbol">(</a><a id="2570" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="2572" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="2574" href="Relation.Binary.Structures.html#1648" class="Function">Equiv.trans</a> <a id="2586" href="Categories.Category.Monoidal.Core.html#2777" class="Field">assoc-commute-from</a>
|
|||
|
|
<a id="2653" class="Symbol">(</a><a id="2654" href="Categories.Category.Core.html#1597" class="Function">∘-resp-≈ˡ</a> <a id="2664" class="Symbol">(</a><a id="2665" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a> <a id="2674" href="Categories.Category.Monoidal.Core.html#1355" class="Field">⊗</a> <a id="2676" class="Symbol">(</a><a id="2677" href="Relation.Binary.Structures.html#1596" class="Function">Equiv.refl</a> <a id="2688" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="2690" href="Categories.Functor.Core.html#511" class="Field">identity</a> <a id="2699" href="Categories.Category.Monoidal.Core.html#1355" class="Field">⊗</a><a id="2700" class="Symbol">)))</a> <a id="2704" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a><a id="2705" class="Symbol">))</a>
|
|||
|
|
<a id="2714" class="Keyword">where</a> <a id="2720" class="Keyword">open</a> <a id="2725" href="Categories.Morphism.Reasoning.html" class="Module">MR</a> <a id="2728" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a>
|
|||
|
|
|
|||
|
|
<a id="2738" href="Categories.Category.Monoidal.Properties.html#2738" class="Function">[uλ]Y</a> <a id="2744" class="Symbol">:</a> <a id="2746" class="Symbol">(</a><a id="2747" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2752" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2755" class="Symbol">(</a><a id="2756" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2761" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2764" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="2765" class="Symbol">))</a> <a id="2768" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2771" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="2773" href="Categories.Category.Core.html#575" class="Function Operator">≅</a> <a id="2775" class="Symbol">(</a><a id="2776" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2781" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2784" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="2785" class="Symbol">)</a> <a id="2787" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2790" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a>
|
|||
|
|
<a id="2796" href="Categories.Category.Monoidal.Properties.html#2738" class="Function">[uλ]Y</a> <a id="2802" class="Symbol">=</a> <a id="2804" class="Symbol">(</a><a id="2805" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="2809" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="2812" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a><a id="2819" class="Symbol">)</a> <a id="2821" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="2824" href="Categories.Category.Core.html#630" class="Function">idᵢ</a>
|
|||
|
|
|
|||
|
|
<a id="2833" href="Categories.Category.Monoidal.Properties.html#2833" class="Function">aY</a> <a id="2836" class="Symbol">:</a> <a id="2838" class="Symbol">((</a><a id="2840" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2845" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2848" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="2852" class="Symbol">)</a> <a id="2854" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2857" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="2858" class="Symbol">)</a> <a id="2860" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2863" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="2865" href="Categories.Category.Core.html#575" class="Function Operator">≅</a> <a id="2867" class="Symbol">(</a><a id="2868" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2873" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2876" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2881" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2884" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="2885" class="Symbol">)</a> <a id="2887" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2890" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a>
|
|||
|
|
<a id="2896" href="Categories.Category.Monoidal.Properties.html#2833" class="Function">aY</a> <a id="2899" class="Symbol">=</a> <a id="2901" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="2912" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="2915" href="Categories.Category.Core.html#630" class="Function">idᵢ</a>
|
|||
|
|
|
|||
|
|
<a id="2924" href="Categories.Category.Monoidal.Properties.html#2924" class="Function">[ρX]Y</a> <a id="2930" class="Symbol">:</a> <a id="2932" class="Symbol">((</a><a id="2934" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2939" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2942" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="2946" class="Symbol">)</a> <a id="2948" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2951" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="2952" class="Symbol">)</a> <a id="2954" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2957" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="2959" href="Categories.Category.Core.html#575" class="Function Operator">≅</a> <a id="2961" class="Symbol">(</a><a id="2962" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="2967" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2970" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="2971" class="Symbol">)</a> <a id="2973" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="2976" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a>
|
|||
|
|
<a id="2982" href="Categories.Category.Monoidal.Properties.html#2924" class="Function">[ρX]Y</a> <a id="2988" class="Symbol">=</a> <a id="2990" class="Symbol">(</a><a id="2991" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="2999" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="3002" href="Categories.Category.Core.html#630" class="Function">idᵢ</a><a id="3005" class="Symbol">)</a> <a id="3007" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="3010" href="Categories.Category.Core.html#630" class="Function">idᵢ</a>
|
|||
|
|
|
|||
|
|
<a id="3019" href="Categories.Category.Monoidal.Properties.html#3019" class="Function">tri</a> <a id="3023" class="Symbol">:</a> <a id="3025" href="Categories.Category.Monoidal.Properties.html#2738" class="Function">[uλ]Y</a> <a id="3031" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="3034" href="Categories.Category.Monoidal.Properties.html#2833" class="Function">aY</a> <a id="3037" href="Categories.Category.Core.html#595" class="Function Operator">≈ᵢ</a> <a id="3040" href="Categories.Category.Monoidal.Properties.html#2924" class="Function">[ρX]Y</a>
|
|||
|
|
<a id="3050" href="Categories.Category.Monoidal.Properties.html#3019" class="Function">tri</a> <a id="3054" class="Symbol">=</a> <a id="3056" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="3058" href="Categories.Functor.Properties.html#2211" class="Function Operator">[</a> <a id="3060" href="Categories.Functor.Bifunctor.html#938" class="Function">appʳ</a> <a id="3065" href="Categories.Category.Monoidal.Core.html#1355" class="Field">⊗</a> <a id="3067" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="3069" href="Categories.Functor.Properties.html#2211" class="Function Operator">]-resp-∘</a> <a id="3078" href="Categories.Category.Monoidal.Core.html#2943" class="Field">triangle</a> <a id="3087" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
|
|||
|
|
|
|||
|
|
<a id="3094" href="Categories.Category.Monoidal.Properties.html#3094" class="Function">sq</a> <a id="3097" class="Symbol">:</a> <a id="3099" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="3110" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="3113" href="Categories.Category.Monoidal.Properties.html#2738" class="Function">[uλ]Y</a> <a id="3119" href="Categories.Category.Core.html#595" class="Function Operator">≈ᵢ</a> <a id="3122" href="Categories.Category.Monoidal.Properties.html#1978" class="Function">u[λY]</a> <a id="3128" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="3131" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a>
|
|||
|
|
<a id="3146" href="Categories.Category.Monoidal.Properties.html#3094" class="Function">sq</a> <a id="3149" class="Symbol">=</a> <a id="3151" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="3153" href="Categories.Category.Monoidal.Core.html#2777" class="Field">assoc-commute-from</a> <a id="3172" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
|
|||
|
|
|
|||
|
|
<a id="3179" class="Comment">-- proofs</a>
|
|||
|
|
|
|||
|
|
<a id="3194" href="Categories.Category.Monoidal.Properties.html#3194" class="Function">perimeter′</a> <a id="3205" class="Symbol">:</a> <a id="3207" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="3209" class="Symbol">((</a><a id="3211" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="3216" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3219" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="3223" class="Symbol">)</a> <a id="3225" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3228" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="3229" class="Symbol">)</a> <a id="3231" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3234" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="3236" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="3238" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="3243" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3246" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="3248" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3251" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="3253" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="3275" class="Symbol">(</a><a id="3276" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="3284" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="3287" href="Categories.Category.Core.html#630" class="Function">idᵢ</a><a id="3290" class="Symbol">)</a> <a id="3292" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="3295" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="3302" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="3305" class="Symbol">(</a><a id="3306" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="3311" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3314" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="3315" class="Symbol">)</a> <a id="3317" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3320" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="3322" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="3343" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a>
|
|||
|
|
<a id="3371" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="3373" href="Categories.Category.Monoidal.Properties.html#2833" class="Function">aY</a> <a id="3400" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="3403" class="Symbol">(</a><a id="3404" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="3409" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3412" class="Symbol">(</a><a id="3413" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="3418" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3421" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="3422" class="Symbol">))</a> <a id="3425" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3428" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="3430" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="3451" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="3478" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="3481" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="3486" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3489" class="Symbol">(</a><a id="3490" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="3495" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3498" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="3499" class="Symbol">)</a> <a id="3501" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3504" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="3506" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="3527" href="Categories.Category.Monoidal.Properties.html#1891" class="Function">ua</a> <a id="3554" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="3557" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="3562" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3565" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="3570" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3573" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="3575" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3578" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="3580" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="3601" href="Categories.Category.Monoidal.Properties.html#2067" class="Function">uλ</a>
|
|||
|
|
<a id="3621" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="3627" href="Categories.Category.Monoidal.Properties.html#3194" class="Function">perimeter′</a> <a id="3638" class="Symbol">=</a> <a id="3640" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
|||
|
|
<a id="3652" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="3663" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="3666" class="Symbol">(</a><a id="3667" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="3675" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="3678" href="Categories.Category.Core.html#630" class="Function">idᵢ</a><a id="3681" class="Symbol">)</a> <a id="3683" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="3686" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="3693" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3696" href="Categories.Category.Monoidal.Properties.html#2156" class="Function">perimeter</a> <a id="3706" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="3714" href="Categories.Category.Monoidal.Properties.html#2067" class="Function">uλ</a> <a id="3717" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="3720" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="3731" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="3734" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="3755" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="3759" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="3767" href="Categories.Category.Monoidal.Utilities.html#4075" class="Function">pentagon-iso</a> <a id="3780" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
|
|||
|
|
<a id="3788" href="Categories.Category.Monoidal.Properties.html#2067" class="Function">uλ</a> <a id="3791" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="3794" href="Categories.Category.Monoidal.Properties.html#1891" class="Function">ua</a> <a id="3797" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="3800" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="3811" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="3814" href="Categories.Category.Monoidal.Properties.html#2833" class="Function">aY</a> <a id="3829" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
|
|||
|
|
|
|||
|
|
<a id="3836" href="Categories.Category.Monoidal.Properties.html#3836" class="Function">top-face</a> <a id="3845" class="Symbol">:</a> <a id="3847" href="Categories.Category.Monoidal.Properties.html#2067" class="Function">uλ</a> <a id="3850" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="3853" href="Categories.Category.Monoidal.Properties.html#1891" class="Function">ua</a> <a id="3856" href="Categories.Category.Core.html#595" class="Function Operator">≈ᵢ</a> <a id="3859" href="Categories.Category.Monoidal.Properties.html#1978" class="Function">u[λY]</a>
|
|||
|
|
<a id="3869" href="Categories.Category.Monoidal.Properties.html#3836" class="Function">top-face</a> <a id="3878" class="Symbol">=</a> <a id="3880" href="Categories.Morphism.Isomorphism.html#8476" class="Function">elim-triangleˡ′</a> <a id="3896" class="Symbol">(</a><a id="3897" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="3899" href="Categories.Category.Monoidal.Properties.html#3194" class="Function">perimeter′</a><a id="3909" class="Symbol">)</a> <a id="3911" class="Symbol">(</a><a id="3912" href="Categories.Morphism.Reasoning.Core.html#5531" class="Function">glue◽◃</a> <a id="3919" class="Symbol">(</a><a id="3920" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="3922" href="Categories.Category.Monoidal.Properties.html#3094" class="Function">sq</a><a id="3924" class="Symbol">)</a> <a id="3926" href="Categories.Category.Monoidal.Properties.html#3019" class="Function">tri</a><a id="3929" class="Symbol">)</a>
|
|||
|
|
<a id="3937" class="Keyword">where</a> <a id="3943" class="Keyword">open</a> <a id="3948" href="Categories.Morphism.Reasoning.html" class="Module">MR</a> <a id="3951" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a>
|
|||
|
|
|
|||
|
|
<a id="3961" href="Categories.Category.Monoidal.Properties.html#3961" class="Function">coherence-iso₁</a> <a id="3976" class="Symbol">:</a> <a id="3978" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="3980" class="Symbol">(</a><a id="3981" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="3986" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3989" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="3990" class="Symbol">)</a> <a id="3992" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="3995" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="3997" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="3999" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="4001" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4004" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="4006" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="4032" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="4049" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="4052" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="4057" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4060" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="4062" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4065" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="4067" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="4092" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a>
|
|||
|
|
<a id="4121" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="4123" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="4131" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="4134" href="Categories.Category.Core.html#630" class="Function">idᵢ</a>
|
|||
|
|
<a id="4159" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="4165" href="Categories.Category.Monoidal.Properties.html#3961" class="Function">coherence-iso₁</a> <a id="4180" class="Symbol">=</a> <a id="4182" href="Categories.Morphism.Isomorphism.html#7806" class="Function">triangle-prism</a> <a id="4197" href="Categories.Category.Monoidal.Properties.html#3836" class="Function">top-face</a> <a id="4206" href="Categories.Category.Monoidal.Properties.html#4242" class="Function">square₁</a> <a id="4214" href="Categories.Category.Monoidal.Properties.html#4470" class="Function">square₂</a> <a id="4222" href="Categories.Category.Monoidal.Properties.html#4714" class="Function">square₃</a>
|
|||
|
|
<a id="4236" class="Keyword">where</a> <a id="4242" href="Categories.Category.Monoidal.Properties.html#4242" class="Function">square₁</a> <a id="4250" class="Symbol">:</a> <a id="4252" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="4254" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="4259" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4262" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="4264" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4267" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="4269" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="4271" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="4276" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4279" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="4281" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4284" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="4286" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="4313" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="4321" href="Categories.Category.Groupoid.html#365" class="Function Operator">⁻¹</a> <a id="4324" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="4327" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a>
|
|||
|
|
<a id="4357" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="4359" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="4363" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="4366" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="4374" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="4377" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="4385" href="Categories.Category.Groupoid.html#365" class="Function Operator">⁻¹</a>
|
|||
|
|
<a id="4410" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="4424" href="Categories.Category.Monoidal.Properties.html#4242" class="Function">square₁</a> <a id="4432" class="Symbol">=</a> <a id="4434" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="4436" href="Categories.Category.Monoidal.Core.html#2582" class="Field">unitorˡ-commute-to</a> <a id="4455" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
|
|||
|
|
|
|||
|
|
<a id="4470" href="Categories.Category.Monoidal.Properties.html#4470" class="Function">square₂</a> <a id="4478" class="Symbol">:</a> <a id="4480" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="4482" class="Symbol">(</a><a id="4483" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="4488" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4491" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="4492" class="Symbol">)</a> <a id="4494" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4497" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="4499" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="4501" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="4506" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4509" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="4514" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4517" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="4519" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4522" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="4524" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="4551" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="4559" href="Categories.Category.Groupoid.html#365" class="Function Operator">⁻¹</a> <a id="4562" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="4565" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a>
|
|||
|
|
<a id="4598" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="4600" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="4604" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="4607" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="4618" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="4621" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="4629" href="Categories.Category.Groupoid.html#365" class="Function Operator">⁻¹</a>
|
|||
|
|
<a id="4654" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="4668" href="Categories.Category.Monoidal.Properties.html#4470" class="Function">square₂</a> <a id="4676" class="Symbol">=</a> <a id="4678" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="4680" href="Categories.Category.Monoidal.Core.html#2582" class="Field">unitorˡ-commute-to</a> <a id="4699" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
|
|||
|
|
|
|||
|
|
<a id="4714" href="Categories.Category.Monoidal.Properties.html#4714" class="Function">square₃</a> <a id="4722" class="Symbol">:</a> <a id="4724" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="4726" class="Symbol">(</a><a id="4727" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="4732" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4735" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="4736" class="Symbol">)</a> <a id="4738" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4741" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="4743" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="4745" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="4750" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4753" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="4755" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4758" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="4760" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="4787" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="4795" href="Categories.Category.Groupoid.html#365" class="Function Operator">⁻¹</a> <a id="4798" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="4801" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="4809" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="4812" href="Categories.Category.Core.html#630" class="Function">idᵢ</a>
|
|||
|
|
<a id="4838" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="4840" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="4844" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="4847" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="4855" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="4858" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="4862" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="4865" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="4873" href="Categories.Category.Groupoid.html#365" class="Function Operator">⁻¹</a>
|
|||
|
|
<a id="4898" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="4912" href="Categories.Category.Monoidal.Properties.html#4714" class="Function">square₃</a> <a id="4920" class="Symbol">=</a> <a id="4922" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="4924" href="Categories.Category.Monoidal.Core.html#2582" class="Field">unitorˡ-commute-to</a> <a id="4943" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
|
|||
|
|
|
|||
|
|
<a id="4950" href="Categories.Category.Monoidal.Properties.html#4950" class="Function">coherence₁</a> <a id="4961" class="Symbol">:</a> <a id="4963" href="Categories.Category.html#1379" class="Function Operator">[</a> <a id="4965" class="Symbol">(</a><a id="4966" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="4971" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4974" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="4975" class="Symbol">)</a> <a id="4977" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4980" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="4982" href="Categories.Category.html#1379" class="Function Operator">⇒</a> <a id="4984" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="4986" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="4989" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="4991" href="Categories.Category.html#1379" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="5013" href="Categories.Category.Monoidal.Utilities.html#1596" class="Function">α⇒</a> <a id="5030" href="Categories.Category.html#1481" class="Function">⇒⟨</a> <a id="5033" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5038" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5041" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5043" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5046" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="5048" href="Categories.Category.html#1481" class="Function">⟩</a>
|
|||
|
|
<a id="5069" href="Categories.Category.Monoidal.Utilities.html#1458" class="Function">λ⇒</a>
|
|||
|
|
<a id="5089" href="Categories.Category.html#1379" class="Function Operator">≈</a> <a id="5091" href="Categories.Category.Monoidal.Utilities.html#1458" class="Function">λ⇒</a> <a id="5094" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5097" href="Categories.Category.Core.html#630" class="Function">id</a>
|
|||
|
|
<a id="5117" href="Categories.Category.html#1379" class="Function Operator">⟩</a>
|
|||
|
|
<a id="5123" href="Categories.Category.Monoidal.Properties.html#4950" class="Function">coherence₁</a> <a id="5134" class="Symbol">=</a> <a id="5136" href="Categories.Morphism.IsoEquiv.html#1830" class="Field">from-≈</a> <a id="5143" href="Categories.Category.Monoidal.Properties.html#3961" class="Function">coherence-iso₁</a>
|
|||
|
|
|
|||
|
|
<a id="5163" href="Categories.Category.Monoidal.Properties.html#5163" class="Function">coherence-inv₁</a> <a id="5178" class="Symbol">:</a> <a id="5180" href="Categories.Category.html#1379" class="Function Operator">[</a> <a id="5182" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5184" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5187" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="5189" href="Categories.Category.html#1379" class="Function Operator">⇒</a> <a id="5191" class="Symbol">(</a><a id="5192" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5197" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5200" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a><a id="5201" class="Symbol">)</a> <a id="5203" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5206" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="5208" href="Categories.Category.html#1379" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="5234" href="Categories.Category.Monoidal.Utilities.html#1478" class="Function">λ⇐</a> <a id="5251" href="Categories.Category.html#1481" class="Function">⇒⟨</a> <a id="5254" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5259" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5262" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5264" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5267" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="5269" href="Categories.Category.html#1481" class="Function">⟩</a>
|
|||
|
|
<a id="5294" href="Categories.Category.Monoidal.Utilities.html#1647" class="Function">α⇐</a>
|
|||
|
|
<a id="5318" href="Categories.Category.html#1379" class="Function Operator">≈</a> <a id="5320" href="Categories.Category.Monoidal.Utilities.html#1478" class="Function">λ⇐</a> <a id="5323" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="5326" href="Categories.Category.Core.html#630" class="Function">id</a>
|
|||
|
|
<a id="5350" href="Categories.Category.html#1379" class="Function Operator">⟩</a>
|
|||
|
|
<a id="5356" href="Categories.Category.Monoidal.Properties.html#5163" class="Function">coherence-inv₁</a> <a id="5371" class="Symbol">=</a> <a id="5373" href="Categories.Morphism.IsoEquiv.html#1858" class="Function">to-≈</a> <a id="5378" href="Categories.Category.Monoidal.Properties.html#3961" class="Function">coherence-iso₁</a>
|
|||
|
|
|
|||
|
|
<a id="5398" class="Comment">-- another coherence property</a>
|
|||
|
|
|
|||
|
|
<a id="5433" class="Comment">-- TS : the following three commute</a>
|
|||
|
|
|
|||
|
|
<a id="5474" href="Categories.Category.Monoidal.Properties.html#5474" class="Function">ρu</a> <a id="5477" class="Symbol">:</a> <a id="5479" class="Symbol">((</a><a id="5481" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5483" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5486" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="5487" class="Symbol">)</a> <a id="5489" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5492" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="5496" class="Symbol">)</a> <a id="5498" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5501" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5506" href="Categories.Category.Core.html#575" class="Function Operator">≅</a> <a id="5508" class="Symbol">(</a><a id="5509" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5511" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5514" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="5515" class="Symbol">)</a> <a id="5517" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5520" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a>
|
|||
|
|
<a id="5529" href="Categories.Category.Monoidal.Properties.html#5474" class="Function">ρu</a> <a id="5532" class="Symbol">=</a> <a id="5534" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="5542" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="5545" href="Categories.Category.Core.html#630" class="Function">idᵢ</a>
|
|||
|
|
|
|||
|
|
<a id="5554" href="Categories.Category.Monoidal.Properties.html#5554" class="Function">au</a> <a id="5557" class="Symbol">:</a> <a id="5559" class="Symbol">((</a><a id="5561" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5563" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5566" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="5567" class="Symbol">)</a> <a id="5569" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5572" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="5576" class="Symbol">)</a> <a id="5578" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5581" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5586" href="Categories.Category.Core.html#575" class="Function Operator">≅</a> <a id="5588" class="Symbol">(</a><a id="5589" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5591" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5594" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="5596" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5599" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="5603" class="Symbol">)</a> <a id="5605" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5608" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a>
|
|||
|
|
<a id="5617" href="Categories.Category.Monoidal.Properties.html#5554" class="Function">au</a> <a id="5620" class="Symbol">=</a> <a id="5622" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="5633" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="5636" href="Categories.Category.Core.html#630" class="Function">idᵢ</a>
|
|||
|
|
|
|||
|
|
<a id="5645" href="Categories.Category.Monoidal.Properties.html#5645" class="Function">[Xρ]u</a> <a id="5651" class="Symbol">:</a> <a id="5653" class="Symbol">(</a><a id="5654" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5656" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5659" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="5661" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5664" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="5668" class="Symbol">)</a> <a id="5670" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5673" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5678" href="Categories.Category.Core.html#575" class="Function Operator">≅</a> <a id="5680" class="Symbol">(</a><a id="5681" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5683" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5686" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="5687" class="Symbol">)</a> <a id="5689" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5692" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a>
|
|||
|
|
<a id="5701" href="Categories.Category.Monoidal.Properties.html#5645" class="Function">[Xρ]u</a> <a id="5707" class="Symbol">=</a> <a id="5709" class="Symbol">(</a><a id="5710" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="5714" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="5717" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a><a id="5724" class="Symbol">)</a> <a id="5726" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="5729" href="Categories.Category.Core.html#630" class="Function">idᵢ</a>
|
|||
|
|
|
|||
|
|
|
|||
|
|
<a id="5739" href="Categories.Category.Monoidal.Properties.html#5739" class="Function">perimeter″</a> <a id="5750" class="Symbol">:</a> <a id="5752" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="5754" class="Symbol">((</a><a id="5756" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5758" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5761" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="5762" class="Symbol">)</a> <a id="5764" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5767" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="5771" class="Symbol">)</a> <a id="5773" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5776" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5781" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="5783" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5785" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5788" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="5790" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5793" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5798" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="5820" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="5847" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="5850" class="Symbol">(</a><a id="5851" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5853" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5856" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="5857" class="Symbol">)</a> <a id="5859" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5862" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5867" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5870" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5875" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="5896" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="5923" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="5926" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="5928" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5931" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="5933" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5936" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5941" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="5944" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="5949" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="5970" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="5974" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="5977" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="5981" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="5984" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a>
|
|||
|
|
<a id="6009" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="6011" href="Categories.Category.Monoidal.Properties.html#5474" class="Function">ρu</a> <a id="6038" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="6041" class="Symbol">(</a><a id="6042" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="6044" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6047" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="6048" class="Symbol">)</a> <a id="6050" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6053" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="6058" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="6079" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a>
|
|||
|
|
<a id="6107" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="6113" href="Categories.Category.Monoidal.Properties.html#5739" class="Function">perimeter″</a> <a id="6124" class="Symbol">=</a> <a id="6126" href="Categories.Morphism.Reasoning.Core.html#5771" class="Function">glue▹◽</a> <a id="6133" href="Categories.Category.Monoidal.Utilities.html#3894" class="Function">triangle-iso</a> <a id="6146" class="Symbol">(</a><a id="6147" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="6149" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a>
|
|||
|
|
<a id="6159" href="Relation.Binary.Structures.html#1648" class="Function">Equiv.trans</a> <a id="6171" class="Symbol">(</a><a id="6172" href="Categories.Category.Core.html#1706" class="Function">∘-resp-≈ʳ</a> <a id="6182" class="Symbol">(</a><a id="6183" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a> <a id="6192" href="Categories.Category.Monoidal.Core.html#1355" class="Field">⊗</a> <a id="6194" class="Symbol">(</a><a id="6195" href="Relation.Binary.Structures.html#1622" class="Function">Equiv.sym</a> <a id="6205" class="Symbol">(</a><a id="6206" href="Categories.Functor.Core.html#511" class="Field">identity</a> <a id="6215" href="Categories.Category.Monoidal.Core.html#1355" class="Field">⊗</a><a id="6216" class="Symbol">)</a> <a id="6218" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="6220" href="Relation.Binary.Structures.html#1596" class="Function">Equiv.refl</a><a id="6230" class="Symbol">)))</a>
|
|||
|
|
<a id="6255" href="Categories.Category.Monoidal.Core.html#2777" class="Field">assoc-commute-from</a> <a id="6274" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a><a id="6275" class="Symbol">)</a>
|
|||
|
|
<a id="6283" class="Keyword">where</a> <a id="6289" class="Keyword">open</a> <a id="6294" href="Categories.Morphism.Reasoning.html" class="Module">MR</a> <a id="6297" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a>
|
|||
|
|
|
|||
|
|
<a id="6307" href="Categories.Category.Monoidal.Properties.html#6307" class="Function">perimeter‴</a> <a id="6318" class="Symbol">:</a> <a id="6320" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="6322" class="Symbol">((</a><a id="6324" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="6326" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6329" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="6330" class="Symbol">)</a> <a id="6332" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6335" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="6339" class="Symbol">)</a> <a id="6341" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6344" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="6349" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="6351" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="6353" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6356" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="6358" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6361" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="6367" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="6389" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="6400" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6403" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6416" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="6419" class="Symbol">(</a><a id="6420" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="6422" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6425" class="Symbol">(</a><a id="6426" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="6428" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6431" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="6435" class="Symbol">))</a> <a id="6438" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6441" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="6446" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="6467" class="Symbol">(</a><a id="6468" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="6494" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="6497" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="6499" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6502" class="Symbol">(</a><a id="6503" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="6505" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6508" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="6512" class="Symbol">)</a> <a id="6514" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6517" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="6522" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="6543" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6547" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6550" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="6570" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="6573" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="6575" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6578" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="6580" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6583" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="6588" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6591" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="6596" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="6617" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6621" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6624" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6628" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6631" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a><a id="6638" class="Symbol">)</a>
|
|||
|
|
<a id="6657" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="6659" href="Categories.Category.Monoidal.Properties.html#5474" class="Function">ρu</a> <a id="6686" href="Categories.Category.Construction.Core.html#1464" class="Function">≅⟨</a> <a id="6689" class="Symbol">(</a><a id="6690" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="6692" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6695" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="6696" class="Symbol">)</a> <a id="6698" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="6701" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="6706" href="Categories.Category.Construction.Core.html#1464" class="Function">⟩</a>
|
|||
|
|
<a id="6727" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a>
|
|||
|
|
<a id="6755" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="6761" href="Categories.Category.Monoidal.Properties.html#6307" class="Function">perimeter‴</a> <a id="6772" class="Symbol">=</a> <a id="6774" class="Keyword">let</a> <a id="6778" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="6780" class="Symbol">=</a> <a id="6782" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="6793" class="Keyword">in</a> <a id="6796" class="Keyword">let</a> <a id="6800" href="Categories.Category.Monoidal.Properties.html#6800" class="Bound">λλ</a> <a id="6803" class="Symbol">=</a> <a id="6805" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="6813" class="Keyword">in</a> <a id="6816" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
|||
|
|
<a id="6828" class="Symbol">(</a><a id="6829" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6833" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6836" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6840" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6843" href="Categories.Category.Monoidal.Properties.html#6800" class="Bound">λλ</a> <a id="6846" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="6849" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6853" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6856" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="6858" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="6861" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a><a id="6862" class="Symbol">)</a> <a id="6864" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="6867" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="6869" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6872" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6877" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6880" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="6882" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="6888" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a> <a id="6890" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="6899" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6903" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6906" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6910" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6913" href="Categories.Category.Monoidal.Properties.html#6800" class="Bound">λλ</a> <a id="6916" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="6919" class="Symbol">(</a><a id="6920" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6924" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6927" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="6929" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="6932" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a><a id="6933" class="Symbol">)</a> <a id="6935" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="6938" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="6940" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6943" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6947" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="6950" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="6958" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="6960" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="6966" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a> <a id="6968" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="6977" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6981" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6984" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="6988" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="6991" href="Categories.Category.Monoidal.Properties.html#6800" class="Bound">λλ</a> <a id="6994" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="6997" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7001" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7004" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="7006" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="7009" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="7011" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="7014" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="7016" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7019" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7025" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="7028" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="7036" href="Categories.Category.Monoidal.Utilities.html#4075" class="Function">pentagon-iso</a> <a id="7049" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="7058" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7062" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7065" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7069" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7072" href="Categories.Category.Monoidal.Properties.html#6800" class="Bound">λλ</a> <a id="7075" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="7078" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="7080" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="7083" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="7106" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="7109" href="Categories.Category.Monoidal.Properties.html#5739" class="Function">perimeter″</a> <a id="7120" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="7129" href="Categories.Category.Monoidal.Properties.html#6778" class="Bound">α</a> <a id="7131" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="7134" href="Categories.Category.Monoidal.Properties.html#5474" class="Function">ρu</a> <a id="7177" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
|
|||
|
|
|
|||
|
|
<a id="7184" href="Categories.Category.Monoidal.Properties.html#7184" class="Function">top-face′</a> <a id="7194" class="Symbol">:</a> <a id="7196" href="Categories.Category.Monoidal.Properties.html#5645" class="Function">[Xρ]u</a> <a id="7202" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="7205" href="Categories.Category.Monoidal.Properties.html#5554" class="Function">au</a> <a id="7208" href="Categories.Category.Core.html#595" class="Function Operator">≈ᵢ</a> <a id="7211" href="Categories.Category.Monoidal.Properties.html#5474" class="Function">ρu</a>
|
|||
|
|
<a id="7218" href="Categories.Category.Monoidal.Properties.html#7184" class="Function">top-face′</a> <a id="7228" class="Symbol">=</a> <a id="7230" href="Categories.Morphism.Isomorphism.html#8812" class="Function">cut-squareʳ</a> <a id="7242" href="Categories.Category.Monoidal.Properties.html#6307" class="Function">perimeter‴</a> <a id="7253" class="Symbol">(</a><a id="7254" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="7256" class="Symbol">(</a><a id="7257" href="Categories.Morphism.Reasoning.Core.html#5295" class="Function">glue◃◽′</a> <a id="7265" href="Categories.Category.Monoidal.Properties.html#7336" class="Function">tri′</a> <a id="7270" class="Symbol">(</a><a id="7271" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="7273" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="7275" href="Categories.Category.Monoidal.Core.html#2777" class="Field">assoc-commute-from</a> <a id="7294" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a><a id="7295" class="Symbol">)))</a>
|
|||
|
|
<a id="7305" class="Keyword">where</a> <a id="7311" class="Keyword">open</a> <a id="7316" href="Categories.Morphism.Reasoning.html" class="Module">MR</a> <a id="7319" href="Categories.Category.Construction.Core.html#484" class="Function">Core</a>
|
|||
|
|
<a id="7336" href="Categories.Category.Monoidal.Properties.html#7336" class="Function">tri′</a> <a id="7341" class="Symbol">:</a> <a id="7343" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="7345" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="7347" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7350" class="Symbol">(</a><a id="7351" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="7353" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7356" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="7360" class="Symbol">)</a> <a id="7362" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7365" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="7370" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="7372" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="7374" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7377" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="7379" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7382" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="7387" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="7411" class="Symbol">(</a><a id="7412" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7416" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7419" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7423" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7426" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="7434" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="7437" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7441" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7444" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a><a id="7454" class="Symbol">)</a>
|
|||
|
|
<a id="7475" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="7477" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7481" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7484" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="7492" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7495" href="Categories.Category.Core.html#630" class="Function">idᵢ</a>
|
|||
|
|
<a id="7518" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="7532" href="Categories.Category.Monoidal.Properties.html#7336" class="Function">tri′</a> <a id="7537" class="Symbol">=</a> <a id="7539" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="7541" href="Categories.Functor.Properties.html#2211" class="Function Operator">[</a> <a id="7543" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="7545" href="Categories.Category.Monoidal.Core.html#1600" class="Function Operator">⊗-</a> <a id="7548" href="Categories.Functor.Properties.html#2211" class="Function Operator">]-resp-∘</a> <a id="7557" href="Categories.Category.Monoidal.Core.html#2943" class="Field">triangle</a> <a id="7566" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
|
|||
|
|
|
|||
|
|
<a id="7573" href="Categories.Category.Monoidal.Properties.html#7573" class="Function">coherence-iso₂</a> <a id="7588" class="Symbol">:</a> <a id="7590" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="7592" class="Symbol">(</a><a id="7593" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="7595" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7598" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="7599" class="Symbol">)</a> <a id="7601" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7604" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="7609" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="7611" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="7613" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7616" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="7618" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="7644" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7648" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7651" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="7659" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="7662" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a>
|
|||
|
|
<a id="7694" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="7696" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a>
|
|||
|
|
<a id="7725" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="7731" href="Categories.Category.Monoidal.Properties.html#7573" class="Function">coherence-iso₂</a> <a id="7746" class="Symbol">=</a> <a id="7748" href="Categories.Morphism.Isomorphism.html#7806" class="Function">triangle-prism</a> <a id="7763" href="Categories.Category.Monoidal.Properties.html#7184" class="Function">top-face′</a> <a id="7773" href="Categories.Category.Monoidal.Properties.html#7824" class="Function">square₁</a> <a id="7781" href="Categories.Category.Monoidal.Properties.html#8070" class="Function">square₂</a> <a id="7789" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="7791" href="Categories.Category.Monoidal.Core.html#2712" class="Field">unitorʳ-commute-to</a> <a id="7810" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
|
|||
|
|
<a id="7818" class="Keyword">where</a> <a id="7824" href="Categories.Category.Monoidal.Properties.html#7824" class="Function">square₁</a> <a id="7832" class="Symbol">:</a> <a id="7834" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="7836" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="7838" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7841" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="7843" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7846" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="7851" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="7853" class="Symbol">(</a><a id="7854" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="7856" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7859" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="7860" class="Symbol">)</a> <a id="7862" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="7865" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="7870" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="7897" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="7905" href="Categories.Category.Groupoid.html#365" class="Function Operator">⁻¹</a> <a id="7908" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="7911" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7915" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7918" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a>
|
|||
|
|
<a id="7948" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="7950" class="Symbol">(</a><a id="7951" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7955" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7958" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a><a id="7965" class="Symbol">)</a> <a id="7967" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="7970" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="7974" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="7977" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="7985" href="Categories.Category.Groupoid.html#365" class="Function Operator">⁻¹</a>
|
|||
|
|
<a id="8010" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="8024" href="Categories.Category.Monoidal.Properties.html#7824" class="Function">square₁</a> <a id="8032" class="Symbol">=</a> <a id="8034" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="8036" href="Categories.Category.Monoidal.Core.html#2712" class="Field">unitorʳ-commute-to</a> <a id="8055" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
|
|||
|
|
|
|||
|
|
<a id="8070" href="Categories.Category.Monoidal.Properties.html#8070" class="Function">square₂</a> <a id="8078" class="Symbol">:</a> <a id="8080" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="8082" class="Symbol">(</a><a id="8083" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="8085" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8088" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="8089" class="Symbol">)</a> <a id="8091" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8094" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="8099" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="8101" class="Symbol">(</a><a id="8102" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="8104" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8107" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="8109" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8112" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="8116" class="Symbol">)</a> <a id="8118" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8121" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="8126" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="8153" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="8161" href="Categories.Category.Groupoid.html#365" class="Function Operator">⁻¹</a> <a id="8164" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="8167" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a>
|
|||
|
|
<a id="8200" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="8202" href="Categories.Category.Monoidal.Core.html#1762" class="Field">associator</a> <a id="8213" href="Categories.Category.Monoidal.Utilities.html#3689" class="Function Operator">⊗ᵢ</a> <a id="8216" href="Categories.Category.Core.html#630" class="Function">idᵢ</a> <a id="8220" href="Categories.Category.Core.html#656" class="Function Operator">∘ᵢ</a> <a id="8223" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="8231" href="Categories.Category.Groupoid.html#365" class="Function Operator">⁻¹</a>
|
|||
|
|
<a id="8256" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="8270" href="Categories.Category.Monoidal.Properties.html#8070" class="Function">square₂</a> <a id="8278" class="Symbol">=</a> <a id="8280" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="8282" href="Categories.Category.Monoidal.Core.html#2712" class="Field">unitorʳ-commute-to</a> <a id="8301" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
|
|||
|
|
|
|||
|
|
<a id="8308" href="Categories.Category.Monoidal.Properties.html#8308" class="Function">coherence₂</a> <a id="8319" class="Symbol">:</a> <a id="8321" href="Categories.Category.html#1379" class="Function Operator">[</a> <a id="8323" class="Symbol">(</a><a id="8324" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="8326" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8329" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="8330" class="Symbol">)</a> <a id="8332" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8335" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="8340" href="Categories.Category.html#1379" class="Function Operator">⇒</a> <a id="8342" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="8344" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8347" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="8349" href="Categories.Category.html#1379" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="8371" href="Categories.Category.Monoidal.Utilities.html#1596" class="Function">α⇒</a> <a id="8388" href="Categories.Category.html#1481" class="Function">⇒⟨</a> <a id="8391" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="8393" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8396" class="Symbol">(</a><a id="8397" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="8399" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8402" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="8406" class="Symbol">)</a> <a id="8408" href="Categories.Category.html#1481" class="Function">⟩</a>
|
|||
|
|
<a id="8429" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="8432" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="8435" href="Categories.Category.Monoidal.Utilities.html#1496" class="Function">ρ⇒</a>
|
|||
|
|
<a id="8455" href="Categories.Category.html#1379" class="Function Operator">≈</a> <a id="8457" href="Categories.Category.Monoidal.Utilities.html#1496" class="Function">ρ⇒</a>
|
|||
|
|
<a id="8477" href="Categories.Category.html#1379" class="Function Operator">⟩</a>
|
|||
|
|
<a id="8483" href="Categories.Category.Monoidal.Properties.html#8308" class="Function">coherence₂</a> <a id="8494" class="Symbol">=</a> <a id="8496" href="Categories.Morphism.IsoEquiv.html#1830" class="Field">from-≈</a> <a id="8503" href="Categories.Category.Monoidal.Properties.html#7573" class="Function">coherence-iso₂</a>
|
|||
|
|
|
|||
|
|
<a id="8523" href="Categories.Category.Monoidal.Properties.html#8523" class="Function">coherence-inv₂</a> <a id="8538" class="Symbol">:</a> <a id="8540" href="Categories.Category.html#1379" class="Function Operator">[</a> <a id="8542" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="8544" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8547" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="8554" href="Categories.Category.html#1379" class="Function Operator">⇒</a> <a id="8556" class="Symbol">(</a><a id="8557" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="8559" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8562" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a><a id="8563" class="Symbol">)</a> <a id="8565" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8568" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="8573" href="Categories.Category.html#1379" class="Function Operator">]⟨</a>
|
|||
|
|
<a id="8599" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="8602" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="8605" href="Categories.Category.Monoidal.Utilities.html#1516" class="Function">ρ⇐</a> <a id="8611" href="Categories.Category.html#1481" class="Function">⇒⟨</a> <a id="8614" href="Categories.Category.Monoidal.Properties.html#1805" class="Bound">X</a> <a id="8616" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8619" class="Symbol">(</a><a id="8620" href="Categories.Category.Monoidal.Properties.html#1807" class="Bound">Y</a> <a id="8622" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8625" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a><a id="8629" class="Symbol">)</a> <a id="8631" href="Categories.Category.html#1481" class="Function">⟩</a>
|
|||
|
|
<a id="8656" href="Categories.Category.Monoidal.Utilities.html#1647" class="Function">α⇐</a>
|
|||
|
|
<a id="8680" href="Categories.Category.html#1379" class="Function Operator">≈</a> <a id="8682" href="Categories.Category.Monoidal.Utilities.html#1516" class="Function">ρ⇐</a>
|
|||
|
|
<a id="8706" href="Categories.Category.html#1379" class="Function Operator">⟩</a>
|
|||
|
|
<a id="8712" href="Categories.Category.Monoidal.Properties.html#8523" class="Function">coherence-inv₂</a> <a id="8727" class="Symbol">=</a> <a id="8729" href="Categories.Morphism.IsoEquiv.html#1858" class="Function">to-≈</a> <a id="8734" href="Categories.Category.Monoidal.Properties.html#7573" class="Function">coherence-iso₂</a>
|
|||
|
|
|
|||
|
|
<a id="8752" class="Comment">-- A third coherence condition (Lemma 2.3)</a>
|
|||
|
|
|
|||
|
|
<a id="Kelly's.coherence₃"></a><a id="8798" href="Categories.Category.Monoidal.Properties.html#8798" class="Function">coherence₃</a> <a id="8809" class="Symbol">:</a> <a id="8811" href="Categories.Category.html#1379" class="Function Operator">[</a> <a id="8813" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="8818" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="8821" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="8826" href="Categories.Category.html#1379" class="Function Operator">⇒</a> <a id="8828" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="8833" href="Categories.Category.html#1379" class="Function Operator">]⟨</a> <a id="8836" href="Categories.Category.Monoidal.Utilities.html#1458" class="Function">λ⇒</a> <a id="8839" href="Categories.Category.html#1379" class="Function Operator">≈</a> <a id="8841" href="Categories.Category.Monoidal.Utilities.html#1496" class="Function">ρ⇒</a> <a id="8844" href="Categories.Category.html#1379" class="Function Operator">⟩</a>
|
|||
|
|
<a id="8848" href="Categories.Category.Monoidal.Properties.html#8798" class="Function">coherence₃</a> <a id="8859" class="Symbol">=</a> <a id="8861" href="Categories.NaturalTransformation.NaturalIsomorphism.Properties.html#1621" class="Function">push-eq</a> <a id="8869" href="Categories.Category.Monoidal.Utilities.html#2295" class="Function">unitorˡ-naturalIsomorphism</a> <a id="8896" class="Symbol">(</a><a id="8897" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
|
|||
|
|
<a id="8907" href="Categories.Category.Core.html#630" class="Function">C.id</a> <a id="8912" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="8915" href="Categories.Category.Monoidal.Utilities.html#1458" class="Function">λ⇒</a> <a id="8932" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="8936" href="Categories.Morphism.Reasoning.Core.html#6665" class="Function">cancelʳ</a> <a id="8944" href="Categories.Morphism.html#1612" class="Function">associator.isoʳ</a> <a id="8960" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
|
|||
|
|
<a id="8966" class="Symbol">(</a><a id="8967" href="Categories.Category.Core.html#630" class="Function">C.id</a> <a id="8972" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="8975" href="Categories.Category.Monoidal.Utilities.html#1458" class="Function">λ⇒</a> <a id="8978" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8980" href="Categories.Category.Monoidal.Utilities.html#1596" class="Function">α⇒</a><a id="8982" class="Symbol">)</a> <a id="8984" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="8986" href="Categories.Category.Monoidal.Utilities.html#1647" class="Function">α⇐</a> <a id="8991" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="8994" href="Categories.Category.Monoidal.Core.html#2943" class="Field">triangle</a> <a id="9003" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="9011" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="9017" href="Categories.Category.Monoidal.Utilities.html#1496" class="Function">ρ⇒</a> <a id="9020" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="9023" href="Categories.Category.Core.html#630" class="Function">C.id</a> <a id="9028" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9030" href="Categories.Category.Monoidal.Utilities.html#1647" class="Function">α⇐</a> <a id="9042" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="9045" href="Categories.Category.Monoidal.Utilities.html#1947" class="Function">unitor-coherenceʳ</a> <a id="9063" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="9071" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="9077" href="Categories.Category.Monoidal.Utilities.html#1496" class="Function">ρ⇒</a> <a id="9080" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9082" href="Categories.Category.Monoidal.Utilities.html#1647" class="Function">α⇐</a> <a id="9102" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="9106" href="Categories.Category.Monoidal.Properties.html#8308" class="Function">coherence₂</a> <a id="9117" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="9125" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
|
|||
|
|
<a id="9131" class="Symbol">(</a><a id="9132" href="Categories.Category.Core.html#630" class="Function">C.id</a> <a id="9137" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="9140" href="Categories.Category.Monoidal.Utilities.html#1496" class="Function">ρ⇒</a> <a id="9143" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9145" href="Categories.Category.Monoidal.Utilities.html#1596" class="Function">α⇒</a><a id="9147" class="Symbol">)</a> <a id="9149" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="9151" href="Categories.Category.Monoidal.Utilities.html#1647" class="Function">α⇐</a> <a id="9156" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="9159" href="Categories.Morphism.Reasoning.Core.html#6665" class="Function">cancelʳ</a> <a id="9167" href="Categories.Morphism.html#1612" class="Function">associator.isoʳ</a> <a id="9183" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
|
|||
|
|
<a id="9189" href="Categories.Category.Core.html#630" class="Function">C.id</a> <a id="9194" href="Categories.Category.Monoidal.Core.html#1536" class="Function Operator">⊗₁</a> <a id="9197" href="Categories.Category.Monoidal.Utilities.html#1496" class="Function">ρ⇒</a> <a id="9214" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a><a id="9215" class="Symbol">)</a>
|
|||
|
|
<a id="9221" class="Keyword">where</a>
|
|||
|
|
<a id="9233" class="Keyword">open</a> <a id="9238" href="Categories.Morphism.Reasoning.html" class="Module">MR</a> <a id="9241" href="Categories.Category.Monoidal.Properties.html#206" class="Bound">C</a> <a id="9243" class="Keyword">hiding</a> <a id="9250" class="Symbol">(</a><a id="9251" href="Categories.Morphism.Reasoning.Iso.html#4018" class="Function">push-eq</a><a id="9258" class="Symbol">)</a>
|
|||
|
|
<a id="9266" class="Keyword">open</a> <a id="9271" href="Categories.Category.Core.html#2462" class="Module">C.HomReasoning</a>
|
|||
|
|
|
|||
|
|
<a id="Kelly's.coherence-iso₃"></a><a id="9289" href="Categories.Category.Monoidal.Properties.html#9289" class="Function">coherence-iso₃</a> <a id="9304" class="Symbol">:</a> <a id="9306" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">[</a> <a id="9308" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="9313" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="9316" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="9321" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≅</a> <a id="9323" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="9328" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">]⟨</a> <a id="9331" href="Categories.Category.Monoidal.Core.html#1700" class="Field">unitorˡ</a> <a id="9339" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">≈</a> <a id="9341" href="Categories.Category.Monoidal.Core.html#1731" class="Field">unitorʳ</a> <a id="9349" href="Categories.Category.Construction.Core.html#1425" class="Function Operator">⟩</a>
|
|||
|
|
<a id="9353" href="Categories.Category.Monoidal.Properties.html#9289" class="Function">coherence-iso₃</a> <a id="9368" class="Symbol">=</a> <a id="9370" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="9372" href="Categories.Category.Monoidal.Properties.html#8798" class="Function">coherence₃</a> <a id="9383" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
|
|||
|
|
|
|||
|
|
<a id="Kelly's.coherence-inv₃"></a><a id="9388" href="Categories.Category.Monoidal.Properties.html#9388" class="Function">coherence-inv₃</a> <a id="9403" class="Symbol">:</a> <a id="9405" href="Categories.Category.html#1379" class="Function Operator">[</a> <a id="9407" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="9412" href="Categories.Category.html#1379" class="Function Operator">⇒</a> <a id="9414" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="9419" href="Categories.Category.Monoidal.Core.html#1435" class="Function Operator">⊗₀</a> <a id="9422" href="Categories.Category.Monoidal.Core.html#1380" class="Field">unit</a> <a id="9427" href="Categories.Category.html#1379" class="Function Operator">]⟨</a> <a id="9430" href="Categories.Category.Monoidal.Utilities.html#1478" class="Function">λ⇐</a> <a id="9433" href="Categories.Category.html#1379" class="Function Operator">≈</a> <a id="9435" href="Categories.Category.Monoidal.Utilities.html#1516" class="Function">ρ⇐</a> <a id="9438" href="Categories.Category.html#1379" class="Function Operator">⟩</a>
|
|||
|
|
<a id="9442" href="Categories.Category.Monoidal.Properties.html#9388" class="Function">coherence-inv₃</a> <a id="9457" class="Symbol">=</a> <a id="9459" href="Categories.Morphism.IsoEquiv.html#1858" class="Function">to-≈</a> <a id="9464" href="Categories.Category.Monoidal.Properties.html#9289" class="Function">coherence-iso₃</a>
|
|||
|
|
|
|||
|
|
<a id="9480" class="Keyword">open</a> <a id="9485" href="Categories.Category.Monoidal.Properties.html#1645" class="Module">Kelly's</a> <a id="9493" class="Keyword">public</a> <a id="9500" class="Keyword">using</a>
|
|||
|
|
<a id="9508" class="Symbol">(</a> <a id="9510" href="Categories.Category.Monoidal.Properties.html#4950" class="Function">coherence₁</a><a id="9520" class="Symbol">;</a> <a id="9522" href="Categories.Category.Monoidal.Properties.html#3961" class="Function">coherence-iso₁</a><a id="9536" class="Symbol">;</a> <a id="9538" href="Categories.Category.Monoidal.Properties.html#5163" class="Function">coherence-inv₁</a>
|
|||
|
|
<a id="9555" class="Symbol">;</a> <a id="9557" href="Categories.Category.Monoidal.Properties.html#8308" class="Function">coherence₂</a><a id="9567" class="Symbol">;</a> <a id="9569" href="Categories.Category.Monoidal.Properties.html#7573" class="Function">coherence-iso₂</a><a id="9583" class="Symbol">;</a> <a id="9585" href="Categories.Category.Monoidal.Properties.html#8523" class="Function">coherence-inv₂</a>
|
|||
|
|
<a id="9602" class="Symbol">;</a> <a id="9604" href="Categories.Category.Monoidal.Properties.html#8798" class="Function">coherence₃</a><a id="9614" class="Symbol">;</a> <a id="9616" href="Categories.Category.Monoidal.Properties.html#9289" class="Function">coherence-iso₃</a><a id="9630" class="Symbol">;</a> <a id="9632" href="Categories.Category.Monoidal.Properties.html#9388" class="Function">coherence-inv₃</a>
|
|||
|
|
<a id="9649" class="Symbol">)</a>
|
|||
|
|
</pre></body></html>
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