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25 KiB
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<html><head><meta charset="utf-8"><title>Categories.Category.Construction.EilenbergMoore</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="37" class="Keyword">open</a> <a id="42" class="Keyword">import</a> <a id="49" href="Categories.Category.html" class="Module">Categories.Category</a>
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<a id="69" class="Keyword">open</a> <a id="74" class="Keyword">import</a> <a id="81" href="Categories.Monad.html" class="Module">Categories.Monad</a>
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<a id="99" class="Keyword">module</a> <a id="106" href="Categories.Category.Construction.EilenbergMoore.html" class="Module">Categories.Category.Construction.EilenbergMoore</a> <a id="154" class="Symbol">{</a><a id="155" href="Categories.Category.Construction.EilenbergMoore.html#155" class="Bound">o</a> <a id="157" href="Categories.Category.Construction.EilenbergMoore.html#157" class="Bound">ℓ</a> <a id="159" href="Categories.Category.Construction.EilenbergMoore.html#159" class="Bound">e</a><a id="160" class="Symbol">}</a> <a id="162" class="Symbol">{</a><a id="163" href="Categories.Category.Construction.EilenbergMoore.html#163" class="Bound">C</a> <a id="165" class="Symbol">:</a> <a id="167" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="176" href="Categories.Category.Construction.EilenbergMoore.html#155" class="Bound">o</a> <a id="178" href="Categories.Category.Construction.EilenbergMoore.html#157" class="Bound">ℓ</a> <a id="180" href="Categories.Category.Construction.EilenbergMoore.html#159" class="Bound">e</a><a id="181" class="Symbol">}</a> <a id="183" class="Symbol">(</a><a id="184" href="Categories.Category.Construction.EilenbergMoore.html#184" class="Bound">M</a> <a id="186" class="Symbol">:</a> <a id="188" href="Categories.Monad.html#454" class="Record">Monad</a> <a id="194" href="Categories.Category.Construction.EilenbergMoore.html#163" class="Bound">C</a><a id="195" class="Symbol">)</a> <a id="197" class="Keyword">where</a>
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<a id="204" class="Keyword">open</a> <a id="209" class="Keyword">import</a> <a id="216" href="Level.html" class="Module">Level</a>
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<a id="223" class="Keyword">open</a> <a id="228" class="Keyword">import</a> <a id="235" href="Categories.Morphism.Reasoning.html" class="Module">Categories.Morphism.Reasoning</a> <a id="265" href="Categories.Category.Construction.EilenbergMoore.html#163" class="Bound">C</a>
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<a id="268" class="Keyword">private</a>
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<a id="278" class="Keyword">module</a> <a id="C"></a><a id="285" href="Categories.Category.Construction.EilenbergMoore.html#285" class="Module">C</a> <a id="287" class="Symbol">=</a> <a id="289" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="298" href="Categories.Category.Construction.EilenbergMoore.html#163" class="Bound">C</a>
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<a id="302" class="Keyword">module</a> <a id="M"></a><a id="309" href="Categories.Category.Construction.EilenbergMoore.html#309" class="Module">M</a> <a id="311" class="Symbol">=</a> <a id="313" href="Categories.Monad.html#454" class="Module">Monad</a> <a id="319" href="Categories.Category.Construction.EilenbergMoore.html#184" class="Bound">M</a>
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<a id="323" class="Keyword">open</a> <a id="328" href="Categories.Category.Construction.EilenbergMoore.html#285" class="Module">C</a>
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<a id="332" class="Keyword">open</a> <a id="337" href="Categories.Monad.html#630" class="Module">M.F</a>
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<a id="343" class="Keyword">open</a> <a id="348" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
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<a id="362" class="Keyword">record</a> <a id="Module"></a><a id="369" href="Categories.Category.Construction.EilenbergMoore.html#369" class="Record">Module</a> <a id="376" class="Symbol">:</a> <a id="378" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="382" class="Symbol">(</a><a id="383" href="Categories.Category.Construction.EilenbergMoore.html#155" class="Bound">o</a> <a id="385" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="387" href="Categories.Category.Construction.EilenbergMoore.html#157" class="Bound">ℓ</a> <a id="389" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="391" href="Categories.Category.Construction.EilenbergMoore.html#159" class="Bound">e</a><a id="392" class="Symbol">)</a> <a id="394" class="Keyword">where</a>
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<a id="402" class="Keyword">field</a>
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<a id="Module.A"></a><a id="412" href="Categories.Category.Construction.EilenbergMoore.html#412" class="Field">A</a> <a id="421" class="Symbol">:</a> <a id="423" href="Categories.Category.Core.html#559" class="Function">Obj</a>
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<a id="Module.action"></a><a id="431" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Field">action</a> <a id="440" class="Symbol">:</a> <a id="442" href="Categories.Functor.Core.html#432" class="Function">F₀</a> <a id="445" href="Categories.Category.Construction.EilenbergMoore.html#412" class="Field">A</a> <a id="447" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="449" href="Categories.Category.Construction.EilenbergMoore.html#412" class="Field">A</a>
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<a id="Module.commute"></a><a id="455" href="Categories.Category.Construction.EilenbergMoore.html#455" class="Field">commute</a> <a id="464" class="Symbol">:</a> <a id="466" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Field">action</a> <a id="473" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="475" href="Categories.Functor.Core.html#455" class="Function">F₁</a> <a id="478" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Field">action</a> <a id="485" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="487" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Field">action</a> <a id="494" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="496" href="Categories.NaturalTransformation.Core.html#783" class="Function">M.μ.η</a> <a id="502" href="Categories.Category.Construction.EilenbergMoore.html#412" class="Field">A</a>
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<a id="Module.identity"></a><a id="508" href="Categories.Category.Construction.EilenbergMoore.html#508" class="Field">identity</a> <a id="517" class="Symbol">:</a> <a id="519" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Field">action</a> <a id="526" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="528" href="Categories.NaturalTransformation.Core.html#783" class="Function">M.η.η</a> <a id="534" href="Categories.Category.Construction.EilenbergMoore.html#412" class="Field">A</a> <a id="536" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="538" href="Categories.Category.Core.html#630" class="Function">C.id</a>
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<a id="544" class="Keyword">record</a> <a id="Module⇒"></a><a id="551" href="Categories.Category.Construction.EilenbergMoore.html#551" class="Record">Module⇒</a> <a id="559" class="Symbol">(</a><a id="560" href="Categories.Category.Construction.EilenbergMoore.html#560" class="Bound">X</a> <a id="562" href="Categories.Category.Construction.EilenbergMoore.html#562" class="Bound">Y</a> <a id="564" class="Symbol">:</a> <a id="566" href="Categories.Category.Construction.EilenbergMoore.html#369" class="Record">Module</a><a id="572" class="Symbol">)</a> <a id="574" class="Symbol">:</a> <a id="576" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="580" class="Symbol">(</a><a id="581" href="Categories.Category.Construction.EilenbergMoore.html#157" class="Bound">ℓ</a> <a id="583" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="585" href="Categories.Category.Construction.EilenbergMoore.html#159" class="Bound">e</a><a id="586" class="Symbol">)</a> <a id="588" class="Keyword">where</a>
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<a id="596" class="Keyword">private</a>
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<a id="608" class="Keyword">module</a> <a id="Module⇒.X"></a><a id="615" href="Categories.Category.Construction.EilenbergMoore.html#615" class="Module">X</a> <a id="617" class="Symbol">=</a> <a id="619" href="Categories.Category.Construction.EilenbergMoore.html#369" class="Module">Module</a> <a id="626" href="Categories.Category.Construction.EilenbergMoore.html#560" class="Bound">X</a>
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<a id="632" class="Keyword">module</a> <a id="Module⇒.Y"></a><a id="639" href="Categories.Category.Construction.EilenbergMoore.html#639" class="Module">Y</a> <a id="641" class="Symbol">=</a> <a id="643" href="Categories.Category.Construction.EilenbergMoore.html#369" class="Module">Module</a> <a id="650" href="Categories.Category.Construction.EilenbergMoore.html#562" class="Bound">Y</a>
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<a id="654" class="Keyword">field</a>
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<a id="Module⇒.arr"></a><a id="664" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">arr</a> <a id="672" class="Symbol">:</a> <a id="674" href="Categories.Category.Construction.EilenbergMoore.html#412" class="Function">X.A</a> <a id="678" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="680" href="Categories.Category.Construction.EilenbergMoore.html#412" class="Function">Y.A</a>
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<a id="Module⇒.commute"></a><a id="688" href="Categories.Category.Construction.EilenbergMoore.html#688" class="Field">commute</a> <a id="696" class="Symbol">:</a> <a id="698" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">arr</a> <a id="702" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="704" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Function">X.action</a> <a id="713" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="715" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Function">Y.action</a> <a id="724" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="726" href="Categories.Functor.Core.html#455" class="Function">F₁</a> <a id="729" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">arr</a>
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<a id="EilenbergMoore"></a><a id="734" href="Categories.Category.Construction.EilenbergMoore.html#734" class="Function">EilenbergMoore</a> <a id="749" class="Symbol">:</a> <a id="751" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="760" class="Symbol">(</a><a id="761" href="Categories.Category.Construction.EilenbergMoore.html#155" class="Bound">o</a> <a id="763" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="765" href="Categories.Category.Construction.EilenbergMoore.html#157" class="Bound">ℓ</a> <a id="767" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="769" href="Categories.Category.Construction.EilenbergMoore.html#159" class="Bound">e</a><a id="770" class="Symbol">)</a> <a id="772" class="Symbol">(</a><a id="773" href="Categories.Category.Construction.EilenbergMoore.html#157" class="Bound">ℓ</a> <a id="775" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="777" href="Categories.Category.Construction.EilenbergMoore.html#159" class="Bound">e</a><a id="778" class="Symbol">)</a> <a id="780" href="Categories.Category.Construction.EilenbergMoore.html#159" class="Bound">e</a>
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||
<a id="782" href="Categories.Category.Construction.EilenbergMoore.html#734" class="Function">EilenbergMoore</a> <a id="797" class="Symbol">=</a> <a id="799" class="Keyword">record</a>
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<a id="808" class="Symbol">{</a> <a id="810" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="820" class="Symbol">=</a> <a id="822" href="Categories.Category.Construction.EilenbergMoore.html#369" class="Record">Module</a>
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<a id="831" class="Symbol">;</a> <a id="833" href="Categories.Category.Core.html#575" class="Field Operator">_⇒_</a> <a id="843" class="Symbol">=</a> <a id="845" href="Categories.Category.Construction.EilenbergMoore.html#551" class="Record">Module⇒</a>
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<a id="855" class="Symbol">;</a> <a id="857" href="Categories.Category.Core.html#595" class="Field Operator">_≈_</a> <a id="867" class="Symbol">=</a> <a id="869" class="Symbol">λ</a> <a id="871" href="Categories.Category.Construction.EilenbergMoore.html#871" class="Bound">f</a> <a id="873" href="Categories.Category.Construction.EilenbergMoore.html#873" class="Bound">g</a> <a id="875" class="Symbol">→</a> <a id="877" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">Module⇒.arr</a> <a id="889" href="Categories.Category.Construction.EilenbergMoore.html#871" class="Bound">f</a> <a id="891" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="893" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">Module⇒.arr</a> <a id="905" href="Categories.Category.Construction.EilenbergMoore.html#873" class="Bound">g</a>
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<a id="909" class="Symbol">;</a> <a id="911" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="921" class="Symbol">=</a> <a id="923" class="Keyword">record</a>
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<a id="934" class="Symbol">{</a> <a id="936" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">arr</a> <a id="944" class="Symbol">=</a> <a id="946" href="Categories.Category.Core.html#630" class="Function">C.id</a>
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<a id="955" class="Symbol">;</a> <a id="957" href="Categories.Category.Construction.EilenbergMoore.html#688" class="Field">commute</a> <a id="965" class="Symbol">=</a> <a id="967" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">id-comm-sym</a> <a id="979" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="981" href="Categories.Category.Core.html#1706" class="Function">∘-resp-≈ʳ</a> <a id="991" class="Symbol">(</a><a id="992" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="994" href="Categories.Functor.Core.html#511" class="Function">identity</a><a id="1002" class="Symbol">)</a>
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<a id="1008" class="Symbol">}</a>
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<a id="1012" class="Symbol">;</a> <a id="1014" href="Categories.Category.Core.html#656" class="Field Operator">_∘_</a> <a id="1024" class="Symbol">=</a> <a id="1026" href="Categories.Category.Construction.EilenbergMoore.html#1302" class="Function">compose</a>
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<a id="1036" class="Symbol">;</a> <a id="1038" href="Categories.Category.Core.html#715" class="Field">assoc</a> <a id="1048" class="Symbol">=</a> <a id="1050" href="Categories.Category.Core.html#715" class="Function">assoc</a>
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||
<a id="1058" class="Symbol">;</a> <a id="1060" href="Categories.Category.Core.html#1004" class="Field">sym-assoc</a> <a id="1070" class="Symbol">=</a> <a id="1072" href="Categories.Category.Core.html#1004" class="Function">sym-assoc</a>
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<a id="1084" class="Symbol">;</a> <a id="1086" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="1096" class="Symbol">=</a> <a id="1098" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a>
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<a id="1110" class="Symbol">;</a> <a id="1112" href="Categories.Category.Core.html#1145" class="Field">identityʳ</a> <a id="1122" class="Symbol">=</a> <a id="1124" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a>
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<a id="1136" class="Symbol">;</a> <a id="1138" href="Categories.Category.Core.html#1339" class="Field">identity²</a> <a id="1148" class="Symbol">=</a> <a id="1150" href="Categories.Category.Core.html#1339" class="Function">identity²</a>
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<a id="1162" class="Symbol">;</a> <a id="1164" href="Categories.Category.Core.html#1384" class="Field">equiv</a> <a id="1174" class="Symbol">=</a> <a id="1176" class="Keyword">record</a>
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<a id="1187" class="Symbol">{</a> <a id="1189" href="Relation.Binary.Structures.html#1577" class="Field">refl</a> <a id="1195" class="Symbol">=</a> <a id="1197" href="Relation.Binary.Structures.html#1577" class="Function">refl</a>
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<a id="1206" class="Symbol">;</a> <a id="1208" href="Relation.Binary.Structures.html#1603" class="Field">sym</a> <a id="1214" class="Symbol">=</a> <a id="1216" href="Relation.Binary.Structures.html#1603" class="Function">sym</a>
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<a id="1224" class="Symbol">;</a> <a id="1226" href="Relation.Binary.Structures.html#1629" class="Field">trans</a> <a id="1232" class="Symbol">=</a> <a id="1234" href="Relation.Binary.Structures.html#1629" class="Function">trans</a>
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<a id="1244" class="Symbol">}</a>
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<a id="1248" class="Symbol">;</a> <a id="1250" href="Categories.Category.Core.html#1438" class="Field">∘-resp-≈</a> <a id="1260" class="Symbol">=</a> <a id="1262" href="Categories.Category.Core.html#1438" class="Function">∘-resp-≈</a>
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||
<a id="1273" class="Symbol">}</a>
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<a id="1277" class="Keyword">where</a>
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||
<a id="1287" class="Keyword">open</a> <a id="1292" href="Categories.Category.Core.html#1530" class="Module">Equiv</a>
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||
<a id="1302" href="Categories.Category.Construction.EilenbergMoore.html#1302" class="Function">compose</a> <a id="1310" class="Symbol">:</a> <a id="1312" class="Symbol">∀</a> <a id="1314" class="Symbol">{</a><a id="1315" href="Categories.Category.Construction.EilenbergMoore.html#1315" class="Bound">X</a> <a id="1317" href="Categories.Category.Construction.EilenbergMoore.html#1317" class="Bound">Y</a> <a id="1319" href="Categories.Category.Construction.EilenbergMoore.html#1319" class="Bound">Z</a><a id="1320" class="Symbol">}</a> <a id="1322" class="Symbol">→</a> <a id="1324" href="Categories.Category.Construction.EilenbergMoore.html#551" class="Record">Module⇒</a> <a id="1332" href="Categories.Category.Construction.EilenbergMoore.html#1317" class="Bound">Y</a> <a id="1334" href="Categories.Category.Construction.EilenbergMoore.html#1319" class="Bound">Z</a> <a id="1336" class="Symbol">→</a> <a id="1338" href="Categories.Category.Construction.EilenbergMoore.html#551" class="Record">Module⇒</a> <a id="1346" href="Categories.Category.Construction.EilenbergMoore.html#1315" class="Bound">X</a> <a id="1348" href="Categories.Category.Construction.EilenbergMoore.html#1317" class="Bound">Y</a> <a id="1350" class="Symbol">→</a> <a id="1352" href="Categories.Category.Construction.EilenbergMoore.html#551" class="Record">Module⇒</a> <a id="1360" href="Categories.Category.Construction.EilenbergMoore.html#1315" class="Bound">X</a> <a id="1362" href="Categories.Category.Construction.EilenbergMoore.html#1319" class="Bound">Z</a>
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<a id="1368" href="Categories.Category.Construction.EilenbergMoore.html#1302" class="Function">compose</a> <a id="1376" class="Symbol">{</a><a id="1377" href="Categories.Category.Construction.EilenbergMoore.html#1377" class="Bound">X</a><a id="1378" class="Symbol">}</a> <a id="1380" class="Symbol">{</a><a id="1381" href="Categories.Category.Construction.EilenbergMoore.html#1381" class="Bound">Y</a><a id="1382" class="Symbol">}</a> <a id="1384" class="Symbol">{</a><a id="1385" href="Categories.Category.Construction.EilenbergMoore.html#1385" class="Bound">Z</a><a id="1386" class="Symbol">}</a> <a id="1388" href="Categories.Category.Construction.EilenbergMoore.html#1388" class="Bound">f</a> <a id="1390" href="Categories.Category.Construction.EilenbergMoore.html#1390" class="Bound">g</a> <a id="1392" class="Symbol">=</a> <a id="1394" class="Keyword">record</a>
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||
<a id="1407" class="Symbol">{</a> <a id="1409" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">arr</a> <a id="1417" class="Symbol">=</a> <a id="1419" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Function">f.arr</a> <a id="1425" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1427" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">g.arr</a>
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||
<a id="1439" class="Symbol">;</a> <a id="1441" href="Categories.Category.Construction.EilenbergMoore.html#688" class="Field">commute</a> <a id="1449" class="Symbol">=</a> <a id="1451" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
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||
<a id="1465" class="Symbol">(</a><a id="1466" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Function">f.arr</a> <a id="1472" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1474" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">g.arr</a><a id="1479" class="Symbol">)</a> <a id="1481" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1483" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Field">Module.action</a> <a id="1497" href="Categories.Category.Construction.EilenbergMoore.html#1377" class="Bound">X</a> <a id="1505" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1508" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="1514" href="Categories.Category.Construction.EilenbergMoore.html#688" class="Field">g.commute</a> <a id="1524" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
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||
<a id="1534" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Function">f.arr</a> <a id="1540" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1542" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Field">Module.action</a> <a id="1556" href="Categories.Category.Construction.EilenbergMoore.html#1381" class="Bound">Y</a> <a id="1558" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1560" href="Categories.Functor.Core.html#455" class="Function">F₁</a> <a id="1563" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">g.arr</a> <a id="1574" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1577" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="1583" href="Categories.Category.Construction.EilenbergMoore.html#688" class="Function">f.commute</a> <a id="1593" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
|
||
<a id="1603" class="Symbol">(</a><a id="1604" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Field">Module.action</a> <a id="1618" href="Categories.Category.Construction.EilenbergMoore.html#1385" class="Bound">Z</a> <a id="1620" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1622" href="Categories.Functor.Core.html#455" class="Function">F₁</a> <a id="1625" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Function">f.arr</a><a id="1630" class="Symbol">)</a> <a id="1632" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1634" href="Categories.Functor.Core.html#455" class="Function">F₁</a> <a id="1637" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">g.arr</a> <a id="1643" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">≈˘⟨</a> <a id="1647" href="Categories.Morphism.Reasoning.Core.html#2347" class="Function">pushʳ</a> <a id="1653" href="Categories.Functor.Core.html#565" class="Function">homomorphism</a> <a id="1666" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">⟩</a>
|
||
<a id="1676" href="Categories.Category.Construction.EilenbergMoore.html#431" class="Field">Module.action</a> <a id="1690" href="Categories.Category.Construction.EilenbergMoore.html#1385" class="Bound">Z</a> <a id="1692" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1694" href="Categories.Functor.Core.html#455" class="Function">F₁</a> <a id="1697" class="Symbol">(</a><a id="1698" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Function">f.arr</a> <a id="1704" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1706" href="Categories.Category.Construction.EilenbergMoore.html#664" class="Field">g.arr</a><a id="1711" class="Symbol">)</a> <a id="1716" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
|
||
<a id="1724" class="Symbol">}</a>
|
||
<a id="1732" class="Keyword">where</a> <a id="1738" class="Keyword">module</a> <a id="1745" href="Categories.Category.Construction.EilenbergMoore.html#1745" class="Module">f</a> <a id="1747" class="Symbol">=</a> <a id="1749" href="Categories.Category.Construction.EilenbergMoore.html#551" class="Module">Module⇒</a> <a id="1757" href="Categories.Category.Construction.EilenbergMoore.html#1388" class="Bound">f</a>
|
||
<a id="1771" class="Keyword">module</a> <a id="1778" href="Categories.Category.Construction.EilenbergMoore.html#1778" class="Module">g</a> <a id="1780" class="Symbol">=</a> <a id="1782" href="Categories.Category.Construction.EilenbergMoore.html#551" class="Module">Module⇒</a> <a id="1790" href="Categories.Category.Construction.EilenbergMoore.html#1390" class="Bound">g</a>
|
||
</pre></body></html> |