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94 lines
42 KiB
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<html><head><meta charset="utf-8"><title>Categories.Functor.Hom</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.Hom.html" class="Module">Categories.Functor.Hom</a> <a id="66" class="Keyword">where</a>
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<a id="73" class="Comment">-- The Hom Functor from C.op × C to Setoids,</a>
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<a id="118" class="Comment">-- the two 1-argument version fixing one object</a>
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<a id="166" class="Comment">-- and some notation for the version where the category must be made explicit</a>
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<a id="245" class="Keyword">open</a> <a id="250" class="Keyword">import</a> <a id="257" href="Data.Product.html" class="Module">Data.Product</a>
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<a id="270" class="Keyword">open</a> <a id="275" class="Keyword">import</a> <a id="282" href="Function.html" class="Module">Function</a> <a id="291" class="Keyword">using</a> <a id="297" class="Symbol">()</a> <a id="300" class="Keyword">renaming</a> <a id="309" class="Symbol">(</a><a id="310" href="Function.Base.html#1040" class="Function Operator">_∘_</a> <a id="314" class="Symbol">to</a> <a id="317" class="Function Operator">_∙_</a><a id="320" class="Symbol">)</a>
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<a id="323" class="Keyword">open</a> <a id="328" class="Keyword">import</a> <a id="335" href="Categories.Category.html" class="Module">Categories.Category</a>
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<a id="355" class="Keyword">open</a> <a id="360" class="Keyword">import</a> <a id="367" href="Categories.Functor.html" class="Module">Categories.Functor</a> <a id="386" class="Keyword">hiding</a> <a id="393" class="Symbol">(</a><a id="394" href="Categories.Functor.html#349" class="Function">id</a><a id="396" class="Symbol">)</a>
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<a id="398" class="Keyword">open</a> <a id="403" class="Keyword">import</a> <a id="410" href="Categories.Functor.Properties.html" class="Module">Categories.Functor.Properties</a>
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<a id="440" class="Keyword">open</a> <a id="445" class="Keyword">import</a> <a id="452" href="Categories.Functor.Bifunctor.html" class="Module">Categories.Functor.Bifunctor</a>
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<a id="481" class="Keyword">open</a> <a id="486" class="Keyword">import</a> <a id="493" href="Categories.Category.Instance.Setoids.html" class="Module">Categories.Category.Instance.Setoids</a>
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<a id="530" class="Keyword">import</a> <a id="537" href="Categories.Morphism.Reasoning.html" class="Module">Categories.Morphism.Reasoning</a> <a id="567" class="Symbol">as</a> <a id="570" class="Module">MR</a>
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<a id="574" class="Keyword">open</a> <a id="579" class="Keyword">import</a> <a id="586" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="602" class="Keyword">using</a> <a id="608" class="Symbol">(</a><a id="609" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a><a id="615" class="Symbol">)</a>
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<a id="618" class="Keyword">module</a> <a id="Hom"></a><a id="625" href="Categories.Functor.Hom.html#625" class="Module">Hom</a> <a id="629" class="Symbol">{</a><a id="630" href="Categories.Functor.Hom.html#630" class="Bound">o</a> <a id="632" href="Categories.Functor.Hom.html#632" class="Bound">ℓ</a> <a id="634" href="Categories.Functor.Hom.html#634" class="Bound">e</a><a id="635" class="Symbol">}</a> <a id="637" class="Symbol">(</a><a id="638" href="Categories.Functor.Hom.html#638" class="Bound">C</a> <a id="640" class="Symbol">:</a> <a id="642" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="651" href="Categories.Functor.Hom.html#630" class="Bound">o</a> <a id="653" href="Categories.Functor.Hom.html#632" class="Bound">ℓ</a> <a id="655" href="Categories.Functor.Hom.html#634" class="Bound">e</a><a id="656" class="Symbol">)</a> <a id="658" class="Keyword">where</a>
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<a id="666" class="Keyword">open</a> <a id="671" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="680" href="Categories.Functor.Hom.html#638" class="Bound">C</a>
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<a id="684" class="Keyword">open</a> <a id="689" href="Categories.Morphism.Reasoning.html" class="Module">MR</a> <a id="692" href="Categories.Functor.Hom.html#638" class="Bound">C</a>
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<a id="Hom.Hom[-,-]"></a><a id="697" href="Categories.Functor.Hom.html#697" class="Function">Hom[-,-]</a> <a id="706" class="Symbol">:</a> <a id="708" href="Categories.Functor.Bifunctor.html#441" class="Function">Bifunctor</a> <a id="718" class="Symbol">(</a><a id="719" href="Categories.Category.Core.html#3132" class="Function">Category.op</a> <a id="731" href="Categories.Functor.Hom.html#638" class="Bound">C</a><a id="732" class="Symbol">)</a> <a id="734" href="Categories.Functor.Hom.html#638" class="Bound">C</a> <a id="736" class="Symbol">(</a><a id="737" href="Categories.Category.Instance.Setoids.html#316" class="Function">Setoids</a> <a id="745" href="Categories.Functor.Hom.html#632" class="Bound">ℓ</a> <a id="747" href="Categories.Functor.Hom.html#634" class="Bound">e</a><a id="748" class="Symbol">)</a>
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<a id="752" href="Categories.Functor.Hom.html#697" class="Function">Hom[-,-]</a> <a id="761" class="Symbol">=</a> <a id="763" class="Keyword">record</a>
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<a id="774" class="Symbol">{</a> <a id="776" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="789" class="Symbol">=</a> <a id="791" href="Categories.Functor.Hom.html#1044" class="Function">F₀′</a>
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<a id="799" class="Symbol">;</a> <a id="801" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="814" class="Symbol">=</a> <a id="816" class="Symbol">λ</a> <a id="818" class="Keyword">where</a>
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<a id="830" class="Symbol">(</a><a id="831" href="Categories.Functor.Hom.html#831" class="Bound">f</a> <a id="833" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="835" href="Categories.Functor.Hom.html#835" class="Bound">g</a><a id="836" class="Symbol">)</a> <a id="838" class="Symbol">→</a> <a id="840" class="Keyword">record</a>
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<a id="855" class="Symbol">{</a> <a id="857" href="Function.Equality.html#1073" class="Field Operator">_⟨$⟩_</a> <a id="863" class="Symbol">=</a> <a id="865" class="Symbol">λ</a> <a id="867" href="Categories.Functor.Hom.html#867" class="Bound">h</a> <a id="869" class="Symbol">→</a> <a id="871" href="Categories.Functor.Hom.html#835" class="Bound">g</a> <a id="873" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="875" href="Categories.Functor.Hom.html#867" class="Bound">h</a> <a id="877" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="879" href="Categories.Functor.Hom.html#831" class="Bound">f</a>
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<a id="889" class="Symbol">;</a> <a id="891" href="Function.Equality.html#1140" class="Field">cong</a> <a id="897" class="Symbol">=</a> <a id="899" href="Categories.Category.Core.html#1706" class="Function">∘-resp-≈ʳ</a> <a id="909" href="Categories.Functor.Hom.html#317" class="Function Operator">∙</a> <a id="911" href="Categories.Category.Core.html#1597" class="Function">∘-resp-≈ˡ</a>
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<a id="929" class="Symbol">}</a>
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<a id="935" class="Symbol">;</a> <a id="937" href="Categories.Functor.Core.html#511" class="Field">identity</a> <a id="950" class="Symbol">=</a> <a id="952" href="Categories.Functor.Hom.html#1155" class="Function">identity′</a>
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<a id="966" class="Symbol">;</a> <a id="968" href="Categories.Functor.Core.html#565" class="Field">homomorphism</a> <a id="981" class="Symbol">=</a> <a id="983" href="Categories.Functor.Hom.html#1423" class="Function">homomorphism′</a>
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<a id="1001" class="Symbol">;</a> <a id="1003" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a> <a id="1016" class="Symbol">=</a> <a id="1018" href="Categories.Functor.Hom.html#2116" class="Function">F-resp-≈′</a>
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<a id="1032" class="Symbol">}</a>
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<a id="1038" class="Keyword">where</a> <a id="1044" href="Categories.Functor.Hom.html#1044" class="Function">F₀′</a> <a id="1048" class="Symbol">:</a> <a id="1050" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="1054" href="Data.Product.html#1176" class="Function Operator">×</a> <a id="1056" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="1060" class="Symbol">→</a> <a id="1062" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a> <a id="1069" href="Categories.Functor.Hom.html#632" class="Bound">ℓ</a> <a id="1071" href="Categories.Functor.Hom.html#634" class="Bound">e</a>
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<a id="1083" href="Categories.Functor.Hom.html#1044" class="Function">F₀′</a> <a id="1087" class="Symbol">(</a><a id="1088" href="Categories.Functor.Hom.html#1088" class="Bound">A</a> <a id="1090" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1092" href="Categories.Functor.Hom.html#1092" class="Bound">B</a><a id="1093" class="Symbol">)</a> <a id="1095" class="Symbol">=</a> <a id="1097" href="Categories.Category.Core.html#1815" class="Function">hom-setoid</a> <a id="1108" class="Symbol">{</a><a id="1109" href="Categories.Functor.Hom.html#1088" class="Bound">A</a><a id="1110" class="Symbol">}</a> <a id="1112" class="Symbol">{</a><a id="1113" href="Categories.Functor.Hom.html#1092" class="Bound">B</a><a id="1114" class="Symbol">}</a>
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<a id="1126" class="Keyword">open</a> <a id="1131" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
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<a id="1155" href="Categories.Functor.Hom.html#1155" class="Function">identity′</a> <a id="1165" class="Symbol">:</a> <a id="1167" class="Symbol">{</a><a id="1168" href="Categories.Functor.Hom.html#1168" class="Bound">A</a> <a id="1170" class="Symbol">:</a> <a id="1172" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="1176" href="Data.Product.html#1176" class="Function Operator">×</a> <a id="1178" href="Categories.Category.Core.html#559" class="Field">Obj</a><a id="1181" class="Symbol">}</a> <a id="1183" class="Symbol">{</a><a id="1184" href="Categories.Functor.Hom.html#1184" class="Bound">x</a> <a id="1186" href="Categories.Functor.Hom.html#1186" class="Bound">y</a> <a id="1188" class="Symbol">:</a> <a id="1190" href="Data.Product.html#3431" class="Function">uncurry</a> <a id="1198" href="Categories.Category.Core.html#575" class="Field Operator">_⇒_</a> <a id="1202" href="Categories.Functor.Hom.html#1168" class="Bound">A</a><a id="1203" class="Symbol">}</a> <a id="1205" class="Symbol">→</a> <a id="1207" href="Categories.Functor.Hom.html#1184" class="Bound">x</a> <a id="1209" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1211" href="Categories.Functor.Hom.html#1186" class="Bound">y</a> <a id="1213" class="Symbol">→</a> <a id="1215" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1218" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1220" href="Categories.Functor.Hom.html#1184" class="Bound">x</a> <a id="1222" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1224" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1227" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1229" href="Categories.Functor.Hom.html#1186" class="Bound">y</a>
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<a id="1241" href="Categories.Functor.Hom.html#1155" class="Function">identity′</a> <a id="1251" class="Symbol">{</a><a id="1252" href="Categories.Functor.Hom.html#1252" class="Bound">A</a><a id="1253" class="Symbol">}</a> <a id="1255" class="Symbol">{</a><a id="1256" href="Categories.Functor.Hom.html#1256" class="Bound">x</a><a id="1257" class="Symbol">}</a> <a id="1259" class="Symbol">{</a><a id="1260" href="Categories.Functor.Hom.html#1260" class="Bound">y</a><a id="1261" class="Symbol">}</a> <a id="1263" href="Categories.Functor.Hom.html#1263" class="Bound">x≈y</a> <a id="1267" class="Symbol">=</a> <a id="1269" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
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<a id="1287" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1290" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1292" href="Categories.Functor.Hom.html#1256" class="Bound">x</a> <a id="1294" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1296" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1299" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1302" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="1312" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
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<a id="1326" href="Categories.Functor.Hom.html#1256" class="Bound">x</a> <a id="1328" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1330" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1338" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1341" href="Categories.Category.Core.html#1145" class="Field">identityʳ</a> <a id="1351" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
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<a id="1365" href="Categories.Functor.Hom.html#1256" class="Bound">x</a> <a id="1377" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1380" href="Categories.Functor.Hom.html#1263" class="Bound">x≈y</a> <a id="1384" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
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<a id="1398" href="Categories.Functor.Hom.html#1260" class="Bound">y</a> <a id="1410" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
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<a id="1423" href="Categories.Functor.Hom.html#1423" class="Function">homomorphism′</a> <a id="1437" class="Symbol">:</a> <a id="1439" class="Symbol">∀</a> <a id="1441" class="Symbol">{</a><a id="1442" href="Categories.Functor.Hom.html#1442" class="Bound">X</a> <a id="1444" href="Categories.Functor.Hom.html#1444" class="Bound">Y</a> <a id="1446" href="Categories.Functor.Hom.html#1446" class="Bound">Z</a> <a id="1448" class="Symbol">:</a> <a id="1450" href="Agda.Builtin.Sigma.html#148" class="Record">Σ</a> <a id="1452" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="1456" class="Symbol">(λ</a> <a id="1459" href="Categories.Functor.Hom.html#1459" class="Bound">x</a> <a id="1461" class="Symbol">→</a> <a id="1463" href="Categories.Category.Core.html#559" class="Field">Obj</a><a id="1466" class="Symbol">)}</a>
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<a id="1497" class="Symbol">{</a><a id="1498" href="Categories.Functor.Hom.html#1498" class="Bound">f</a> <a id="1500" class="Symbol">:</a> <a id="1502" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="1508" href="Categories.Functor.Hom.html#1444" class="Bound">Y</a> <a id="1510" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="1512" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="1518" href="Categories.Functor.Hom.html#1442" class="Bound">X</a> <a id="1520" href="Data.Product.html#1176" class="Function Operator">×</a> <a id="1522" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="1528" href="Categories.Functor.Hom.html#1442" class="Bound">X</a> <a id="1530" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="1532" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="1538" href="Categories.Functor.Hom.html#1444" class="Bound">Y</a><a id="1539" class="Symbol">}</a>
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<a id="1569" class="Symbol">{</a><a id="1570" href="Categories.Functor.Hom.html#1570" class="Bound">g</a> <a id="1572" class="Symbol">:</a> <a id="1574" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="1580" href="Categories.Functor.Hom.html#1446" class="Bound">Z</a> <a id="1582" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="1584" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="1590" href="Categories.Functor.Hom.html#1444" class="Bound">Y</a> <a id="1592" href="Data.Product.html#1176" class="Function Operator">×</a> <a id="1594" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="1600" href="Categories.Functor.Hom.html#1444" class="Bound">Y</a> <a id="1602" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="1604" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="1610" href="Categories.Functor.Hom.html#1446" class="Bound">Z</a><a id="1611" class="Symbol">}</a>
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<a id="1641" class="Symbol">{</a><a id="1642" href="Categories.Functor.Hom.html#1642" class="Bound">x</a> <a id="1644" href="Categories.Functor.Hom.html#1644" class="Bound">y</a> <a id="1646" class="Symbol">:</a> <a id="1648" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="1654" href="Categories.Functor.Hom.html#1442" class="Bound">X</a> <a id="1656" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="1658" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="1664" href="Categories.Functor.Hom.html#1442" class="Bound">X</a><a id="1665" class="Symbol">}</a> <a id="1667" class="Symbol">→</a>
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<a id="1697" href="Categories.Functor.Hom.html#1642" class="Bound">x</a> <a id="1699" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1701" href="Categories.Functor.Hom.html#1644" class="Bound">y</a> <a id="1703" class="Symbol">→</a>
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<a id="1733" class="Symbol">(</a><a id="1734" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="1740" href="Categories.Functor.Hom.html#1570" class="Bound">g</a> <a id="1742" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1744" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="1750" href="Categories.Functor.Hom.html#1498" class="Bound">f</a><a id="1751" class="Symbol">)</a> <a id="1753" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1755" href="Categories.Functor.Hom.html#1642" class="Bound">x</a> <a id="1757" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1759" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="1765" href="Categories.Functor.Hom.html#1498" class="Bound">f</a> <a id="1767" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1769" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="1775" href="Categories.Functor.Hom.html#1570" class="Bound">g</a> <a id="1777" href="Categories.Category.Core.html#595" class="Field Operator">≈</a>
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<a id="1807" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="1813" href="Categories.Functor.Hom.html#1570" class="Bound">g</a> <a id="1815" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1817" class="Symbol">(</a><a id="1818" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="1824" href="Categories.Functor.Hom.html#1498" class="Bound">f</a> <a id="1826" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1828" href="Categories.Functor.Hom.html#1644" class="Bound">y</a> <a id="1830" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1832" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="1838" href="Categories.Functor.Hom.html#1498" class="Bound">f</a><a id="1839" class="Symbol">)</a> <a id="1841" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1843" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="1849" href="Categories.Functor.Hom.html#1570" class="Bound">g</a>
|
|||
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<a id="1861" href="Categories.Functor.Hom.html#1423" class="Function">homomorphism′</a> <a id="1875" class="Symbol">{</a><a id="1876" class="Argument">f</a> <a id="1878" class="Symbol">=</a> <a id="1880" href="Categories.Functor.Hom.html#1880" class="Bound">f₁</a> <a id="1883" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1885" href="Categories.Functor.Hom.html#1885" class="Bound">f₂</a><a id="1887" class="Symbol">}</a> <a id="1889" class="Symbol">{</a><a id="1890" href="Categories.Functor.Hom.html#1890" class="Bound">g₁</a> <a id="1893" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1895" href="Categories.Functor.Hom.html#1895" class="Bound">g₂</a><a id="1897" class="Symbol">}</a> <a id="1899" class="Symbol">{</a><a id="1900" href="Categories.Functor.Hom.html#1900" class="Bound">x</a><a id="1901" class="Symbol">}</a> <a id="1903" class="Symbol">{</a><a id="1904" href="Categories.Functor.Hom.html#1904" class="Bound">y</a><a id="1905" class="Symbol">}</a> <a id="1907" href="Categories.Functor.Hom.html#1907" class="Bound">x≈y</a> <a id="1911" class="Symbol">=</a> <a id="1913" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
|
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<a id="1931" class="Symbol">(</a><a id="1932" href="Categories.Functor.Hom.html#1895" class="Bound">g₂</a> <a id="1935" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1937" href="Categories.Functor.Hom.html#1885" class="Bound">f₂</a><a id="1939" class="Symbol">)</a> <a id="1941" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1943" href="Categories.Functor.Hom.html#1900" class="Bound">x</a> <a id="1945" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1947" href="Categories.Functor.Hom.html#1880" class="Bound">f₁</a> <a id="1950" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1952" href="Categories.Functor.Hom.html#1890" class="Bound">g₁</a> <a id="1957" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1960" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="1968" href="Categories.Category.Core.html#1004" class="Field">sym-assoc</a> <a id="1978" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
|
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|
<a id="1992" class="Symbol">(</a><a id="1993" href="Categories.Functor.Hom.html#1895" class="Bound">g₂</a> <a id="1996" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1998" href="Categories.Functor.Hom.html#1885" class="Bound">f₂</a><a id="2000" class="Symbol">)</a> <a id="2002" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2004" class="Symbol">(</a><a id="2005" href="Categories.Functor.Hom.html#1900" class="Bound">x</a> <a id="2007" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2009" href="Categories.Functor.Hom.html#1880" class="Bound">f₁</a><a id="2011" class="Symbol">)</a> <a id="2013" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2015" href="Categories.Functor.Hom.html#1890" class="Bound">g₁</a> <a id="2018" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="2021" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="2027" class="Symbol">(</a><a id="2028" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="2034" class="Symbol">(</a><a id="2035" href="Categories.Category.Core.html#1706" class="Function">∘-resp-≈ʳ</a> <a id="2045" class="Symbol">(</a><a id="2046" href="Categories.Category.Core.html#1597" class="Function">∘-resp-≈ˡ</a> <a id="2056" href="Categories.Functor.Hom.html#1907" class="Bound">x≈y</a><a id="2059" class="Symbol">)))</a> <a id="2063" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
|
|||
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<a id="2077" href="Categories.Functor.Hom.html#1895" class="Bound">g₂</a> <a id="2080" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2082" class="Symbol">(</a><a id="2083" href="Categories.Functor.Hom.html#1885" class="Bound">f₂</a> <a id="2086" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2088" href="Categories.Functor.Hom.html#1904" class="Bound">y</a> <a id="2090" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2092" href="Categories.Functor.Hom.html#1880" class="Bound">f₁</a><a id="2094" class="Symbol">)</a> <a id="2096" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2098" href="Categories.Functor.Hom.html#1890" class="Bound">g₁</a> <a id="2103" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
|
|||
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|
|||
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<a id="2116" href="Categories.Functor.Hom.html#2116" class="Function">F-resp-≈′</a> <a id="2126" class="Symbol">:</a> <a id="2128" class="Symbol">∀</a> <a id="2130" class="Symbol">{</a><a id="2131" href="Categories.Functor.Hom.html#2131" class="Bound">A</a> <a id="2133" href="Categories.Functor.Hom.html#2133" class="Bound">B</a> <a id="2135" class="Symbol">:</a> <a id="2137" href="Agda.Builtin.Sigma.html#148" class="Record">Σ</a> <a id="2139" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="2143" class="Symbol">(λ</a> <a id="2146" href="Categories.Functor.Hom.html#2146" class="Bound">x</a> <a id="2148" class="Symbol">→</a> <a id="2150" href="Categories.Category.Core.html#559" class="Field">Obj</a><a id="2153" class="Symbol">)}</a>
|
|||
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|
<a id="2180" class="Symbol">{</a><a id="2181" href="Categories.Functor.Hom.html#2181" class="Bound">f</a> <a id="2183" href="Categories.Functor.Hom.html#2183" class="Bound">g</a> <a id="2185" class="Symbol">:</a> <a id="2187" href="Agda.Builtin.Sigma.html#148" class="Record">Σ</a> <a id="2189" class="Symbol">(</a><a id="2190" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="2196" href="Categories.Functor.Hom.html#2133" class="Bound">B</a> <a id="2198" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="2200" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="2206" href="Categories.Functor.Hom.html#2131" class="Bound">A</a><a id="2207" class="Symbol">)</a> <a id="2209" class="Symbol">(λ</a> <a id="2212" href="Categories.Functor.Hom.html#2212" class="Bound">x</a> <a id="2214" class="Symbol">→</a> <a id="2216" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="2222" href="Categories.Functor.Hom.html#2131" class="Bound">A</a> <a id="2224" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="2226" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="2232" href="Categories.Functor.Hom.html#2133" class="Bound">B</a><a id="2233" class="Symbol">)}</a> <a id="2236" class="Symbol">→</a>
|
|||
|
|
<a id="2262" href="Agda.Builtin.Sigma.html#148" class="Record">Σ</a> <a id="2264" class="Symbol">(</a><a id="2265" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="2271" href="Categories.Functor.Hom.html#2181" class="Bound">f</a> <a id="2273" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="2275" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="2281" href="Categories.Functor.Hom.html#2183" class="Bound">g</a><a id="2282" class="Symbol">)</a> <a id="2284" class="Symbol">(λ</a> <a id="2287" href="Categories.Functor.Hom.html#2287" class="Bound">x</a> <a id="2289" class="Symbol">→</a> <a id="2291" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="2297" href="Categories.Functor.Hom.html#2181" class="Bound">f</a> <a id="2299" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="2301" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="2307" href="Categories.Functor.Hom.html#2183" class="Bound">g</a><a id="2308" class="Symbol">)</a> <a id="2310" class="Symbol">→</a>
|
|||
|
|
<a id="2336" class="Symbol">{</a><a id="2337" href="Categories.Functor.Hom.html#2337" class="Bound">x</a> <a id="2339" href="Categories.Functor.Hom.html#2339" class="Bound">y</a> <a id="2341" class="Symbol">:</a> <a id="2343" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="2349" href="Categories.Functor.Hom.html#2131" class="Bound">A</a> <a id="2351" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="2353" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="2359" href="Categories.Functor.Hom.html#2131" class="Bound">A</a><a id="2360" class="Symbol">}</a> <a id="2362" class="Symbol">→</a>
|
|||
|
|
<a id="2388" href="Categories.Functor.Hom.html#2337" class="Bound">x</a> <a id="2390" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="2392" href="Categories.Functor.Hom.html#2339" class="Bound">y</a> <a id="2394" class="Symbol">→</a> <a id="2396" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="2402" href="Categories.Functor.Hom.html#2181" class="Bound">f</a> <a id="2404" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2406" href="Categories.Functor.Hom.html#2337" class="Bound">x</a> <a id="2408" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2410" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="2416" href="Categories.Functor.Hom.html#2181" class="Bound">f</a> <a id="2418" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="2420" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a> <a id="2426" href="Categories.Functor.Hom.html#2183" class="Bound">g</a> <a id="2428" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2430" href="Categories.Functor.Hom.html#2339" class="Bound">y</a> <a id="2432" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2434" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a> <a id="2440" href="Categories.Functor.Hom.html#2183" class="Bound">g</a>
|
|||
|
|
<a id="2452" href="Categories.Functor.Hom.html#2116" class="Function">F-resp-≈′</a> <a id="2462" class="Symbol">{</a><a id="2463" class="Argument">f</a> <a id="2465" class="Symbol">=</a> <a id="2467" href="Categories.Functor.Hom.html#2467" class="Bound">f₁</a> <a id="2470" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="2472" href="Categories.Functor.Hom.html#2472" class="Bound">f₂</a><a id="2474" class="Symbol">}</a> <a id="2476" class="Symbol">{</a><a id="2477" href="Categories.Functor.Hom.html#2477" class="Bound">g₁</a> <a id="2480" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="2482" href="Categories.Functor.Hom.html#2482" class="Bound">g₂</a><a id="2484" class="Symbol">}</a> <a id="2486" class="Symbol">(</a><a id="2487" href="Categories.Functor.Hom.html#2487" class="Bound">f₁≈g₁</a> <a id="2493" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="2495" href="Categories.Functor.Hom.html#2495" class="Bound">f₂≈g₂</a><a id="2500" class="Symbol">)</a> <a id="2502" class="Symbol">{</a><a id="2503" href="Categories.Functor.Hom.html#2503" class="Bound">x</a><a id="2504" class="Symbol">}</a> <a id="2506" class="Symbol">{</a><a id="2507" href="Categories.Functor.Hom.html#2507" class="Bound">y</a><a id="2508" class="Symbol">}</a> <a id="2510" href="Categories.Functor.Hom.html#2510" class="Bound">x≈y</a> <a id="2514" class="Symbol">=</a> <a id="2516" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
|
|||
|
|
<a id="2534" href="Categories.Functor.Hom.html#2472" class="Bound">f₂</a> <a id="2537" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2539" href="Categories.Functor.Hom.html#2503" class="Bound">x</a> <a id="2541" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2543" href="Categories.Functor.Hom.html#2467" class="Bound">f₁</a> <a id="2546" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="2549" href="Categories.Functor.Hom.html#2495" class="Bound">f₂≈g₂</a> <a id="2555" href="Categories.Category.Core.html#2634" class="Function Operator">⟩∘⟨</a> <a id="2559" href="Categories.Functor.Hom.html#2510" class="Bound">x≈y</a> <a id="2563" href="Categories.Category.Core.html#2634" class="Function Operator">⟩∘⟨</a> <a id="2567" href="Categories.Functor.Hom.html#2487" class="Bound">f₁≈g₁</a> <a id="2573" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
|
|||
|
|
<a id="2587" href="Categories.Functor.Hom.html#2482" class="Bound">g₂</a> <a id="2590" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2592" href="Categories.Functor.Hom.html#2507" class="Bound">y</a> <a id="2594" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2596" href="Categories.Functor.Hom.html#2477" class="Bound">g₁</a> <a id="2599" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
|
|||
|
|
|
|||
|
|
<a id="Hom.Hom[_,-]"></a><a id="2604" href="Categories.Functor.Hom.html#2604" class="Function Operator">Hom[_,-]</a> <a id="2613" class="Symbol">:</a> <a id="2615" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="2619" class="Symbol">→</a> <a id="2621" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="2629" href="Categories.Functor.Hom.html#638" class="Bound">C</a> <a id="2631" class="Symbol">(</a><a id="2632" href="Categories.Category.Instance.Setoids.html#316" class="Function">Setoids</a> <a id="2640" href="Categories.Functor.Hom.html#632" class="Bound">ℓ</a> <a id="2642" href="Categories.Functor.Hom.html#634" class="Bound">e</a><a id="2643" class="Symbol">)</a>
|
|||
|
|
<a id="2647" href="Categories.Functor.Hom.html#2604" class="Function Operator">Hom[_,-]</a> <a id="2656" class="Symbol">=</a> <a id="2658" href="Categories.Functor.Bifunctor.html#874" class="Function">appˡ</a> <a id="2663" href="Categories.Functor.Hom.html#697" class="Function">Hom[-,-]</a>
|
|||
|
|
|
|||
|
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<a id="Hom.Hom[-,_]"></a><a id="2675" href="Categories.Functor.Hom.html#2675" class="Function Operator">Hom[-,_]</a> <a id="2684" class="Symbol">:</a> <a id="2686" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="2690" class="Symbol">→</a> <a id="2692" href="Categories.Functor.Properties.html#855" class="Function">Contravariant</a> <a id="2706" href="Categories.Functor.Hom.html#638" class="Bound">C</a> <a id="2708" class="Symbol">(</a><a id="2709" href="Categories.Category.Instance.Setoids.html#316" class="Function">Setoids</a> <a id="2717" href="Categories.Functor.Hom.html#632" class="Bound">ℓ</a> <a id="2719" href="Categories.Functor.Hom.html#634" class="Bound">e</a><a id="2720" class="Symbol">)</a>
|
|||
|
|
<a id="2724" href="Categories.Functor.Hom.html#2675" class="Function Operator">Hom[-,_]</a> <a id="2733" class="Symbol">=</a> <a id="2735" href="Categories.Functor.Bifunctor.html#938" class="Function">appʳ</a> <a id="2740" href="Categories.Functor.Hom.html#697" class="Function">Hom[-,-]</a>
|
|||
|
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|
|||
|
|
<a id="Hom.Hom[_,_]"></a><a id="2752" href="Categories.Functor.Hom.html#2752" class="Function Operator">Hom[_,_]</a> <a id="2761" class="Symbol">:</a> <a id="2763" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="2767" class="Symbol">→</a> <a id="2769" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="2773" class="Symbol">→</a> <a id="2775" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a> <a id="2782" href="Categories.Functor.Hom.html#632" class="Bound">ℓ</a> <a id="2784" href="Categories.Functor.Hom.html#634" class="Bound">e</a>
|
|||
|
|
<a id="2788" href="Categories.Functor.Hom.html#2752" class="Function Operator">Hom[</a> <a id="2793" href="Categories.Functor.Hom.html#2793" class="Bound">A</a> <a id="2795" href="Categories.Functor.Hom.html#2752" class="Function Operator">,</a> <a id="2797" href="Categories.Functor.Hom.html#2797" class="Bound">B</a> <a id="2799" href="Categories.Functor.Hom.html#2752" class="Function Operator">]</a> <a id="2801" class="Symbol">=</a> <a id="2803" href="Categories.Category.Core.html#1815" class="Function">hom-setoid</a> <a id="2814" class="Symbol">{</a><a id="2815" href="Categories.Functor.Hom.html#2793" class="Bound">A</a><a id="2816" class="Symbol">}</a> <a id="2818" class="Symbol">{</a><a id="2819" href="Categories.Functor.Hom.html#2797" class="Bound">B</a><a id="2820" class="Symbol">}</a>
|
|||
|
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|
|||
|
|
<a id="2823" class="Comment">-- Notation for when the ambient Category must be specified explicitly.</a>
|
|||
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<a id="2895" class="Keyword">module</a> <a id="2902" href="Categories.Functor.Hom.html#2902" class="Module">_</a> <a id="2904" class="Symbol">{</a><a id="2905" href="Categories.Functor.Hom.html#2905" class="Bound">o</a> <a id="2907" href="Categories.Functor.Hom.html#2907" class="Bound">ℓ</a> <a id="2909" href="Categories.Functor.Hom.html#2909" class="Bound">e</a><a id="2910" class="Symbol">}</a> <a id="2912" class="Symbol">(</a><a id="2913" href="Categories.Functor.Hom.html#2913" class="Bound">C</a> <a id="2915" class="Symbol">:</a> <a id="2917" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="2926" href="Categories.Functor.Hom.html#2905" class="Bound">o</a> <a id="2928" href="Categories.Functor.Hom.html#2907" class="Bound">ℓ</a> <a id="2930" href="Categories.Functor.Hom.html#2909" class="Bound">e</a><a id="2931" class="Symbol">)</a> <a id="2933" class="Keyword">where</a>
|
|||
|
|
<a id="2941" class="Keyword">open</a> <a id="2946" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="2955" href="Categories.Functor.Hom.html#2913" class="Bound">C</a>
|
|||
|
|
<a id="2959" class="Keyword">open</a> <a id="2964" href="Categories.Functor.Hom.html#625" class="Module">Hom</a> <a id="2968" href="Categories.Functor.Hom.html#2913" class="Bound">C</a>
|
|||
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|
|||
|
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<a id="2973" href="Categories.Functor.Hom.html#2973" class="Function Operator">Hom[_][-,-]</a> <a id="2985" class="Symbol">:</a> <a id="2987" href="Categories.Functor.Bifunctor.html#441" class="Function">Bifunctor</a> <a id="2997" class="Symbol">(</a><a id="2998" href="Categories.Category.Core.html#3132" class="Function">Category.op</a> <a id="3010" href="Categories.Functor.Hom.html#2913" class="Bound">C</a><a id="3011" class="Symbol">)</a> <a id="3013" href="Categories.Functor.Hom.html#2913" class="Bound">C</a> <a id="3015" class="Symbol">(</a><a id="3016" href="Categories.Category.Instance.Setoids.html#316" class="Function">Setoids</a> <a id="3024" href="Categories.Functor.Hom.html#2907" class="Bound">ℓ</a> <a id="3026" href="Categories.Functor.Hom.html#2909" class="Bound">e</a><a id="3027" class="Symbol">)</a>
|
|||
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<a id="3031" href="Categories.Functor.Hom.html#2973" class="Function Operator">Hom[_][-,-]</a> <a id="3043" class="Symbol">=</a> <a id="3045" href="Categories.Functor.Hom.html#697" class="Function">Hom[-,-]</a>
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<a id="3057" href="Categories.Functor.Hom.html#3057" class="Function Operator">Hom[_][_,-]</a> <a id="3069" class="Symbol">:</a> <a id="3071" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="3075" class="Symbol">→</a> <a id="3077" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="3085" href="Categories.Functor.Hom.html#2913" class="Bound">C</a> <a id="3087" class="Symbol">(</a><a id="3088" href="Categories.Category.Instance.Setoids.html#316" class="Function">Setoids</a> <a id="3096" href="Categories.Functor.Hom.html#2907" class="Bound">ℓ</a> <a id="3098" href="Categories.Functor.Hom.html#2909" class="Bound">e</a><a id="3099" class="Symbol">)</a>
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<a id="3103" href="Categories.Functor.Hom.html#3057" class="Function Operator">Hom[_][_,-]</a> <a id="3115" href="Categories.Functor.Hom.html#3115" class="Bound">B</a> <a id="3117" class="Symbol">=</a> <a id="3119" href="Categories.Functor.Hom.html#2604" class="Function Operator">Hom[</a> <a id="3124" href="Categories.Functor.Hom.html#3115" class="Bound">B</a> <a id="3126" href="Categories.Functor.Hom.html#2604" class="Function Operator">,-]</a>
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<a id="3133" href="Categories.Functor.Hom.html#3133" class="Function Operator">Hom[_][-,_]</a> <a id="3145" class="Symbol">:</a> <a id="3147" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="3151" class="Symbol">→</a> <a id="3153" href="Categories.Functor.Properties.html#855" class="Function">Contravariant</a> <a id="3167" href="Categories.Functor.Hom.html#2913" class="Bound">C</a> <a id="3169" class="Symbol">(</a><a id="3170" href="Categories.Category.Instance.Setoids.html#316" class="Function">Setoids</a> <a id="3178" href="Categories.Functor.Hom.html#2907" class="Bound">ℓ</a> <a id="3180" href="Categories.Functor.Hom.html#2909" class="Bound">e</a><a id="3181" class="Symbol">)</a>
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<a id="3185" href="Categories.Functor.Hom.html#3133" class="Function Operator">Hom[_][-,_]</a> <a id="3197" href="Categories.Functor.Hom.html#3197" class="Bound">B</a> <a id="3199" class="Symbol">=</a> <a id="3201" href="Categories.Functor.Hom.html#2675" class="Function Operator">Hom[-,</a> <a id="3208" href="Categories.Functor.Hom.html#3197" class="Bound">B</a> <a id="3210" href="Categories.Functor.Hom.html#2675" class="Function Operator">]</a>
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<a id="3215" href="Categories.Functor.Hom.html#3215" class="Function Operator">Hom[_][_,_]</a> <a id="3227" class="Symbol">:</a> <a id="3229" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="3233" class="Symbol">→</a> <a id="3235" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="3239" class="Symbol">→</a> <a id="3241" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a> <a id="3248" href="Categories.Functor.Hom.html#2907" class="Bound">ℓ</a> <a id="3250" href="Categories.Functor.Hom.html#2909" class="Bound">e</a>
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<a id="3254" href="Categories.Functor.Hom.html#3215" class="Function Operator">Hom[_][_,_]</a> <a id="3266" href="Categories.Functor.Hom.html#3266" class="Bound">A</a> <a id="3268" href="Categories.Functor.Hom.html#3268" class="Bound">B</a> <a id="3270" class="Symbol">=</a> <a id="3272" href="Categories.Category.Core.html#1815" class="Function">hom-setoid</a> <a id="3283" class="Symbol">{</a><a id="3284" href="Categories.Functor.Hom.html#3266" class="Bound">A</a><a id="3285" class="Symbol">}</a> <a id="3287" class="Symbol">{</a><a id="3288" href="Categories.Functor.Hom.html#3268" class="Bound">B</a><a id="3289" class="Symbol">}</a>
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</pre></body></html>
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