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61 lines
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<html><head><meta charset="utf-8"><title>Categories.Functor</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">module</a> <a id="43" href="Categories.Functor.html" class="Module">Categories.Functor</a> <a id="62" class="Keyword">where</a>
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<a id="69" class="Keyword">open</a> <a id="74" class="Keyword">import</a> <a id="81" href="Level.html" class="Module">Level</a>
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<a id="87" class="Keyword">open</a> <a id="92" class="Keyword">import</a> <a id="99" href="Function.html" class="Module">Function</a> <a id="108" class="Keyword">renaming</a> <a id="117" class="Symbol">(</a><a id="118" href="Function.Base.html#624" class="Function">id</a> <a id="121" class="Symbol">to</a> <a id="124" class="Function">id→</a><a id="127" class="Symbol">;</a> <a id="129" href="Function.Base.html#1040" class="Function Operator">_∘_</a> <a id="133" class="Symbol">to</a> <a id="136" class="Function Operator">_●_</a><a id="139" class="Symbol">)</a> <a id="141" class="Keyword">using</a> <a id="147" class="Symbol">()</a>
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<a id="151" class="Keyword">open</a> <a id="156" class="Keyword">import</a> <a id="163" href="Categories.Category.html" class="Module">Categories.Category</a>
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<a id="183" class="Keyword">open</a> <a id="188" class="Keyword">import</a> <a id="195" href="Categories.Functor.Core.html" class="Module">Categories.Functor.Core</a> <a id="219" class="Keyword">public</a>
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<a id="227" class="Keyword">private</a>
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<a id="237" class="Keyword">variable</a>
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<a id="250" href="Categories.Functor.html#250" class="Generalizable">o</a> <a id="252" href="Categories.Functor.html#252" class="Generalizable">ℓ</a> <a id="254" href="Categories.Functor.html#254" class="Generalizable">e</a> <a id="256" href="Categories.Functor.html#256" class="Generalizable">o′</a> <a id="259" href="Categories.Functor.html#259" class="Generalizable">ℓ′</a> <a id="262" href="Categories.Functor.html#262" class="Generalizable">e′</a> <a id="265" href="Categories.Functor.html#265" class="Generalizable">o″</a> <a id="268" href="Categories.Functor.html#268" class="Generalizable">ℓ″</a> <a id="271" href="Categories.Functor.html#271" class="Generalizable">e″</a> <a id="274" class="Symbol">:</a> <a id="276" href="Agda.Primitive.html#591" class="Postulate">Level</a>
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<a id="Endofunctor"></a><a id="283" href="Categories.Functor.html#283" class="Function">Endofunctor</a> <a id="295" class="Symbol">:</a> <a id="297" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="306" href="Categories.Functor.html#250" class="Generalizable">o</a> <a id="308" href="Categories.Functor.html#252" class="Generalizable">ℓ</a> <a id="310" href="Categories.Functor.html#254" class="Generalizable">e</a> <a id="312" class="Symbol">→</a> <a id="314" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="318" class="Symbol">_</a>
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<a id="320" href="Categories.Functor.html#283" class="Function">Endofunctor</a> <a id="332" href="Categories.Functor.html#332" class="Bound">C</a> <a id="334" class="Symbol">=</a> <a id="336" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="344" href="Categories.Functor.html#332" class="Bound">C</a> <a id="346" href="Categories.Functor.html#332" class="Bound">C</a>
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<a id="id"></a><a id="349" href="Categories.Functor.html#349" class="Function">id</a> <a id="352" class="Symbol">:</a> <a id="354" class="Symbol">∀</a> <a id="356" class="Symbol">{</a><a id="357" href="Categories.Functor.html#357" class="Bound">C</a> <a id="359" class="Symbol">:</a> <a id="361" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="370" href="Categories.Functor.html#250" class="Generalizable">o</a> <a id="372" href="Categories.Functor.html#252" class="Generalizable">ℓ</a> <a id="374" href="Categories.Functor.html#254" class="Generalizable">e</a><a id="375" class="Symbol">}</a> <a id="377" class="Symbol">→</a> <a id="379" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="387" href="Categories.Functor.html#357" class="Bound">C</a> <a id="389" href="Categories.Functor.html#357" class="Bound">C</a>
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<a id="391" href="Categories.Functor.html#349" class="Function">id</a> <a id="394" class="Symbol">{</a><a id="395" class="Argument">C</a> <a id="397" class="Symbol">=</a> <a id="399" href="Categories.Functor.html#399" class="Bound">C</a><a id="400" class="Symbol">}</a> <a id="402" class="Symbol">=</a> <a id="404" class="Keyword">record</a>
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<a id="413" class="Symbol">{</a> <a id="415" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="428" class="Symbol">=</a> <a id="430" href="Categories.Functor.html#124" class="Function">id→</a>
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<a id="436" class="Symbol">;</a> <a id="438" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="451" class="Symbol">=</a> <a id="453" href="Categories.Functor.html#124" class="Function">id→</a>
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<a id="459" class="Symbol">;</a> <a id="461" href="Categories.Functor.Core.html#511" class="Field">identity</a> <a id="474" class="Symbol">=</a> <a id="476" href="Relation.Binary.Structures.html#1577" class="Function">Category.Equiv.refl</a> <a id="496" href="Categories.Functor.html#399" class="Bound">C</a>
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<a id="500" class="Symbol">;</a> <a id="502" href="Categories.Functor.Core.html#565" class="Field">homomorphism</a> <a id="515" class="Symbol">=</a> <a id="517" href="Relation.Binary.Structures.html#1577" class="Function">Category.Equiv.refl</a> <a id="537" href="Categories.Functor.html#399" class="Bound">C</a>
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<a id="541" class="Symbol">;</a> <a id="543" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a> <a id="556" class="Symbol">=</a> <a id="558" href="Categories.Functor.html#124" class="Function">id→</a>
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<a id="564" class="Symbol">}</a>
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<a id="567" class="Keyword">infixr</a> <a id="574" class="Number">9</a> <a id="576" href="Categories.Functor.html#747" class="Function Operator">_∘F_</a>
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<a id="582" class="Comment">-- note that this definition could be shortened by inlining the definitions for</a>
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<a id="662" class="Comment">-- identity′ and homomorphism′, but the definitions below are simpler to understand.</a>
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<a id="_∘F_"></a><a id="747" href="Categories.Functor.html#747" class="Function Operator">_∘F_</a> <a id="752" class="Symbol">:</a> <a id="754" class="Symbol">∀</a> <a id="756" class="Symbol">{</a><a id="757" href="Categories.Functor.html#757" class="Bound">C</a> <a id="759" class="Symbol">:</a> <a id="761" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="770" href="Categories.Functor.html#250" class="Generalizable">o</a> <a id="772" href="Categories.Functor.html#252" class="Generalizable">ℓ</a> <a id="774" href="Categories.Functor.html#254" class="Generalizable">e</a><a id="775" class="Symbol">}</a> <a id="777" class="Symbol">{</a><a id="778" href="Categories.Functor.html#778" class="Bound">D</a> <a id="780" class="Symbol">:</a> <a id="782" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="791" href="Categories.Functor.html#256" class="Generalizable">o′</a> <a id="794" href="Categories.Functor.html#259" class="Generalizable">ℓ′</a> <a id="797" href="Categories.Functor.html#262" class="Generalizable">e′</a><a id="799" class="Symbol">}</a> <a id="801" class="Symbol">{</a><a id="802" href="Categories.Functor.html#802" class="Bound">E</a> <a id="804" class="Symbol">:</a> <a id="806" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="815" href="Categories.Functor.html#265" class="Generalizable">o″</a> <a id="818" href="Categories.Functor.html#268" class="Generalizable">ℓ″</a> <a id="821" href="Categories.Functor.html#271" class="Generalizable">e″</a><a id="823" class="Symbol">}</a>
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<a id="829" class="Symbol">→</a> <a id="831" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="839" href="Categories.Functor.html#778" class="Bound">D</a> <a id="841" href="Categories.Functor.html#802" class="Bound">E</a> <a id="843" class="Symbol">→</a> <a id="845" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="853" href="Categories.Functor.html#757" class="Bound">C</a> <a id="855" href="Categories.Functor.html#778" class="Bound">D</a> <a id="857" class="Symbol">→</a> <a id="859" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="867" href="Categories.Functor.html#757" class="Bound">C</a> <a id="869" href="Categories.Functor.html#802" class="Bound">E</a>
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<a id="871" href="Categories.Functor.html#747" class="Function Operator">_∘F_</a> <a id="876" class="Symbol">{</a><a id="877" class="Argument">C</a> <a id="879" class="Symbol">=</a> <a id="881" href="Categories.Functor.html#881" class="Bound">C</a><a id="882" class="Symbol">}</a> <a id="884" class="Symbol">{</a><a id="885" class="Argument">D</a> <a id="887" class="Symbol">=</a> <a id="889" href="Categories.Functor.html#889" class="Bound">D</a><a id="890" class="Symbol">}</a> <a id="892" class="Symbol">{</a><a id="893" class="Argument">E</a> <a id="895" class="Symbol">=</a> <a id="897" href="Categories.Functor.html#897" class="Bound">E</a><a id="898" class="Symbol">}</a> <a id="900" href="Categories.Functor.html#900" class="Bound">F</a> <a id="902" href="Categories.Functor.html#902" class="Bound">G</a> <a id="904" class="Symbol">=</a> <a id="906" class="Keyword">record</a>
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<a id="915" class="Symbol">{</a> <a id="917" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="920" class="Symbol">=</a> <a id="922" href="Categories.Functor.Core.html#797" class="Function">F.₀</a> <a id="926" href="Categories.Functor.html#136" class="Function Operator">●</a> <a id="928" href="Categories.Functor.Core.html#797" class="Function">G.₀</a>
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<a id="934" class="Symbol">;</a> <a id="936" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="939" class="Symbol">=</a> <a id="941" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="945" href="Categories.Functor.html#136" class="Function Operator">●</a> <a id="947" href="Categories.Functor.Core.html#806" class="Function">G.₁</a>
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<a id="953" class="Symbol">;</a> <a id="955" href="Categories.Functor.Core.html#511" class="Field">identity</a> <a id="964" class="Symbol">=</a> <a id="966" href="Categories.Functor.html#1236" class="Function">identity′</a>
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<a id="978" class="Symbol">;</a> <a id="980" href="Categories.Functor.Core.html#565" class="Field">homomorphism</a> <a id="993" class="Symbol">=</a> <a id="995" href="Categories.Functor.html#1445" class="Function">homomorphism′</a>
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<a id="1011" class="Symbol">;</a> <a id="1013" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a> <a id="1022" class="Symbol">=</a> <a id="1025" href="Categories.Functor.Core.html#696" class="Function">F.F-resp-≈</a> <a id="1036" href="Categories.Functor.html#136" class="Function Operator">●</a> <a id="1038" href="Categories.Functor.Core.html#696" class="Field">G.F-resp-≈</a>
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<a id="1051" class="Symbol">}</a>
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<a id="1055" class="Keyword">where</a>
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<a id="1063" class="Keyword">module</a> <a id="1070" href="Categories.Functor.html#1070" class="Module">C</a> <a id="1072" class="Symbol">=</a> <a id="1074" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="1083" href="Categories.Functor.html#881" class="Bound">C</a> <a id="1085" class="Keyword">using</a> <a id="1091" class="Symbol">(</a><a id="1092" href="Categories.Category.Core.html#630" class="Field">id</a><a id="1094" class="Symbol">)</a>
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<a id="1098" class="Keyword">module</a> <a id="1105" href="Categories.Functor.html#1105" class="Module">D</a> <a id="1107" class="Symbol">=</a> <a id="1109" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="1118" href="Categories.Functor.html#889" class="Bound">D</a> <a id="1120" class="Keyword">using</a> <a id="1126" class="Symbol">(</a><a id="1127" href="Categories.Category.Core.html#630" class="Field">id</a><a id="1129" class="Symbol">)</a>
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<a id="1133" class="Keyword">module</a> <a id="1140" href="Categories.Functor.html#1140" class="Module">E</a> <a id="1142" class="Symbol">=</a> <a id="1144" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="1153" href="Categories.Functor.html#897" class="Bound">E</a> <a id="1155" class="Keyword">using</a> <a id="1161" class="Symbol">(</a><a id="1162" href="Categories.Category.Core.html#630" class="Field">id</a><a id="1164" class="Symbol">;</a> <a id="1166" class="Keyword">module</a> <a id="1173" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a><a id="1185" class="Symbol">)</a>
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<a id="1189" class="Keyword">module</a> <a id="1196" href="Categories.Functor.html#1196" class="Module">F</a> <a id="1198" class="Symbol">=</a> <a id="1200" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="1208" href="Categories.Functor.html#900" class="Bound">F</a>
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<a id="1212" class="Keyword">module</a> <a id="1219" href="Categories.Functor.html#1219" class="Module">G</a> <a id="1221" class="Symbol">=</a> <a id="1223" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="1231" href="Categories.Functor.html#902" class="Bound">G</a>
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<a id="1236" href="Categories.Functor.html#1236" class="Function">identity′</a> <a id="1246" class="Symbol">:</a> <a id="1248" class="Symbol">∀</a> <a id="1250" class="Symbol">{</a><a id="1251" href="Categories.Functor.html#1251" class="Bound">A</a><a id="1252" class="Symbol">}</a> <a id="1254" class="Symbol">→</a> <a id="1256" href="Categories.Functor.html#897" class="Bound">E</a> <a id="1258" href="Categories.Category.html#609" class="Function Operator">[</a> <a id="1260" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="1264" class="Symbol">(</a><a id="1265" href="Categories.Functor.Core.html#806" class="Function">G.₁</a> <a id="1269" class="Symbol">(</a><a id="1270" href="Categories.Category.Core.html#630" class="Function">C.id</a> <a id="1275" class="Symbol">{</a><a id="1276" href="Categories.Functor.html#1251" class="Bound">A</a><a id="1277" class="Symbol">}))</a> <a id="1281" href="Categories.Category.html#609" class="Function Operator">≈</a> <a id="1283" href="Categories.Category.Core.html#630" class="Function">E.id</a> <a id="1288" href="Categories.Category.html#609" class="Function Operator">]</a>
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<a id="1292" href="Categories.Functor.html#1236" class="Function">identity′</a> <a id="1302" class="Symbol">=</a> <a id="1304" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
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<a id="1314" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="1318" class="Symbol">(</a><a id="1319" href="Categories.Functor.Core.html#806" class="Function">G.₁</a> <a id="1323" href="Categories.Category.Core.html#630" class="Function">C.id</a><a id="1327" class="Symbol">)</a> <a id="1329" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1332" href="Categories.Functor.Core.html#696" class="Function">F.F-resp-≈</a> <a id="1343" href="Categories.Functor.Core.html#511" class="Field">G.identity</a> <a id="1354" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
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<a id="1360" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="1364" href="Categories.Category.Core.html#630" class="Function">D.id</a> <a id="1375" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1378" href="Categories.Functor.Core.html#511" class="Function">F.identity</a> <a id="1389" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
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<a id="1395" href="Categories.Category.Core.html#630" class="Function">E.id</a> <a id="1410" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
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<a id="1416" class="Keyword">where</a> <a id="1422" class="Keyword">open</a> <a id="1427" href="Categories.Category.Core.html#2462" class="Module">E.HomReasoning</a>
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<a id="1445" href="Categories.Functor.html#1445" class="Function">homomorphism′</a> <a id="1459" class="Symbol">:</a> <a id="1461" class="Symbol">∀</a> <a id="1463" class="Symbol">{</a><a id="1464" href="Categories.Functor.html#1464" class="Bound">X</a> <a id="1466" href="Categories.Functor.html#1466" class="Bound">Y</a> <a id="1468" href="Categories.Functor.html#1468" class="Bound">Z</a><a id="1469" class="Symbol">}</a> <a id="1471" class="Symbol">{</a><a id="1472" href="Categories.Functor.html#1472" class="Bound">f</a> <a id="1474" class="Symbol">:</a> <a id="1476" href="Categories.Functor.html#881" class="Bound">C</a> <a id="1478" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="1480" href="Categories.Functor.html#1464" class="Bound">X</a> <a id="1482" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="1484" href="Categories.Functor.html#1466" class="Bound">Y</a> <a id="1486" href="Categories.Category.html#502" class="Function Operator">]</a><a id="1487" class="Symbol">}</a> <a id="1489" class="Symbol">{</a><a id="1490" href="Categories.Functor.html#1490" class="Bound">g</a> <a id="1492" class="Symbol">:</a> <a id="1494" href="Categories.Functor.html#881" class="Bound">C</a> <a id="1496" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="1498" href="Categories.Functor.html#1466" class="Bound">Y</a> <a id="1500" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="1502" href="Categories.Functor.html#1468" class="Bound">Z</a> <a id="1504" href="Categories.Category.html#502" class="Function Operator">]</a><a id="1505" class="Symbol">}</a>
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<a id="1524" class="Symbol">→</a> <a id="1526" href="Categories.Functor.html#897" class="Bound">E</a> <a id="1528" href="Categories.Category.html#609" class="Function Operator">[</a> <a id="1530" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="1534" class="Symbol">(</a><a id="1535" href="Categories.Functor.Core.html#806" class="Function">G.₁</a> <a id="1539" class="Symbol">(</a><a id="1540" href="Categories.Functor.html#881" class="Bound">C</a> <a id="1542" href="Categories.Category.html#700" class="Function Operator">[</a> <a id="1544" href="Categories.Functor.html#1490" class="Bound">g</a> <a id="1546" href="Categories.Category.html#700" class="Function Operator">∘</a> <a id="1548" href="Categories.Functor.html#1472" class="Bound">f</a> <a id="1550" href="Categories.Category.html#700" class="Function Operator">]</a><a id="1551" class="Symbol">))</a> <a id="1554" href="Categories.Category.html#609" class="Function Operator">≈</a> <a id="1556" href="Categories.Functor.html#897" class="Bound">E</a> <a id="1558" href="Categories.Category.html#700" class="Function Operator">[</a> <a id="1560" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="1564" class="Symbol">(</a><a id="1565" href="Categories.Functor.Core.html#806" class="Function">G.₁</a> <a id="1569" href="Categories.Functor.html#1490" class="Bound">g</a><a id="1570" class="Symbol">)</a> <a id="1572" href="Categories.Category.html#700" class="Function Operator">∘</a> <a id="1574" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="1578" class="Symbol">(</a><a id="1579" href="Categories.Functor.Core.html#806" class="Function">G.₁</a> <a id="1583" href="Categories.Functor.html#1472" class="Bound">f</a><a id="1584" class="Symbol">)</a> <a id="1586" href="Categories.Category.html#700" class="Function Operator">]</a> <a id="1588" href="Categories.Category.html#609" class="Function Operator">]</a>
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<a id="1592" href="Categories.Functor.html#1445" class="Function">homomorphism′</a> <a id="1606" class="Symbol">{</a><a id="1607" class="Argument">f</a> <a id="1609" class="Symbol">=</a> <a id="1611" href="Categories.Functor.html#1611" class="Bound">f</a><a id="1612" class="Symbol">}</a> <a id="1614" class="Symbol">{</a><a id="1615" class="Argument">g</a> <a id="1617" class="Symbol">=</a> <a id="1619" href="Categories.Functor.html#1619" class="Bound">g</a><a id="1620" class="Symbol">}</a> <a id="1622" class="Symbol">=</a> <a id="1624" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
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<a id="1634" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="1638" class="Symbol">(</a><a id="1639" href="Categories.Functor.Core.html#806" class="Function">G.₁</a> <a id="1643" class="Symbol">(</a><a id="1644" href="Categories.Functor.html#881" class="Bound">C</a> <a id="1646" href="Categories.Category.html#700" class="Function Operator">[</a> <a id="1648" href="Categories.Functor.html#1619" class="Bound">g</a> <a id="1650" href="Categories.Category.html#700" class="Function Operator">∘</a> <a id="1652" href="Categories.Functor.html#1611" class="Bound">f</a> <a id="1654" href="Categories.Category.html#700" class="Function Operator">]</a><a id="1655" class="Symbol">))</a> <a id="1666" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1669" href="Categories.Functor.Core.html#696" class="Function">F.F-resp-≈</a> <a id="1680" href="Categories.Functor.Core.html#565" class="Field">G.homomorphism</a> <a id="1695" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
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<a id="1701" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="1705" class="Symbol">(</a><a id="1706" href="Categories.Functor.html#889" class="Bound">D</a> <a id="1708" href="Categories.Category.html#700" class="Function Operator">[</a> <a id="1710" href="Categories.Functor.Core.html#806" class="Function">G.₁</a> <a id="1714" href="Categories.Functor.html#1619" class="Bound">g</a> <a id="1716" href="Categories.Category.html#700" class="Function Operator">∘</a> <a id="1718" href="Categories.Functor.Core.html#806" class="Function">G.₁</a> <a id="1722" href="Categories.Functor.html#1611" class="Bound">f</a> <a id="1724" href="Categories.Category.html#700" class="Function Operator">]</a><a id="1725" class="Symbol">)</a> <a id="1733" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1736" href="Categories.Functor.Core.html#565" class="Function">F.homomorphism</a> <a id="1751" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
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<a id="1757" href="Categories.Functor.html#897" class="Bound">E</a> <a id="1759" href="Categories.Category.html#700" class="Function Operator">[</a> <a id="1761" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="1765" class="Symbol">(</a><a id="1766" href="Categories.Functor.Core.html#806" class="Function">G.₁</a> <a id="1770" href="Categories.Functor.html#1619" class="Bound">g</a><a id="1771" class="Symbol">)</a> <a id="1773" href="Categories.Category.html#700" class="Function Operator">∘</a> <a id="1775" href="Categories.Functor.Core.html#806" class="Function">F.₁</a> <a id="1779" class="Symbol">(</a><a id="1780" href="Categories.Functor.Core.html#806" class="Function">G.₁</a> <a id="1784" href="Categories.Functor.html#1611" class="Bound">f</a><a id="1785" class="Symbol">)</a> <a id="1787" href="Categories.Category.html#700" class="Function Operator">]</a> <a id="1789" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
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<a id="1795" class="Keyword">where</a> <a id="1801" class="Keyword">open</a> <a id="1806" href="Categories.Category.Core.html#2462" class="Module">E.HomReasoning</a>
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</pre></body></html>
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