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<html><head><meta charset="utf-8"><title>Categories.Morphism.HeterogeneousIdentity.Properties</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Symbol">{-#</a> <a id="5" class="Keyword">OPTIONS</a> <a id="13" class="Pragma">--without-K</a> <a id="25" class="Pragma">--safe</a> <a id="32" class="Symbol">#-}</a>
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<a id="37" class="Comment">-- Some properties of 'heterogeneous' identity morphisms</a>
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<a id="95" class="Keyword">module</a> <a id="102" href="Categories.Morphism.HeterogeneousIdentity.Properties.html" class="Module">Categories.Morphism.HeterogeneousIdentity.Properties</a> <a id="155" class="Keyword">where</a>
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<a id="162" class="Keyword">open</a> <a id="167" class="Keyword">import</a> <a id="174" href="Level.html" class="Module">Level</a>
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<a id="180" class="Keyword">open</a> <a id="185" class="Keyword">import</a> <a id="192" href="Data.Product.html" class="Module">Data.Product</a> <a id="205" class="Keyword">using</a> <a id="211" class="Symbol">(</a><a id="212" href="Data.Product.html#3274" class="Function">curry</a><a id="217" class="Symbol">)</a> <a id="219" class="Keyword">renaming</a> <a id="228" class="Symbol">(</a><a id="229" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">_,_</a> <a id="233" class="Symbol">to</a> <a id="236" class="InductiveConstructor Operator">_,,_</a><a id="240" class="Symbol">)</a>
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<a id="242" class="Keyword">open</a> <a id="247" class="Keyword">import</a> <a id="254" href="Relation.Binary.PropositionalEquality.html" class="Module">Relation.Binary.PropositionalEquality</a>
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<a id="293" class="Keyword">open</a> <a id="298" class="Keyword">import</a> <a id="305" href="Categories.Category.html" class="Module">Categories.Category</a> <a id="325" class="Keyword">using</a> <a id="331" class="Symbol">(</a><a id="332" href="Categories.Category.Core.html#442" class="Record">Category</a><a id="340" class="Symbol">;</a> <a id="342" href="Categories.Category.html#502" class="Function Operator">_[_,_]</a><a id="348" class="Symbol">;</a> <a id="350" href="Categories.Category.html#609" class="Function Operator">_[_≈_]</a><a id="356" class="Symbol">)</a>
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<a id="358" class="Keyword">open</a> <a id="363" class="Keyword">import</a> <a id="370" href="Categories.Category.Product.html" class="Module">Categories.Category.Product</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.html" class="Module">Categories.Functor</a> <a id="429" class="Keyword">using</a> <a id="435" class="Symbol">(</a><a id="436" href="Categories.Functor.Core.html#248" class="Record">Functor</a><a id="443" class="Symbol">)</a> <a id="445" class="Keyword">renaming</a> <a id="454" class="Symbol">(</a><a id="455" href="Categories.Functor.html#349" class="Function">id</a> <a id="458" class="Symbol">to</a> <a id="461" class="Function">idF</a><a id="464" class="Symbol">)</a>
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<a id="466" class="Keyword">open</a> <a id="471" class="Keyword">import</a> <a id="478" href="Categories.Functor.Bifunctor.html" class="Module">Categories.Functor.Bifunctor</a>
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<a id="507" class="Keyword">open</a> <a id="512" class="Keyword">import</a> <a id="519" href="Categories.Morphism.HeterogeneousIdentity.html" class="Module">Categories.Morphism.HeterogeneousIdentity</a>
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<a id="562" class="Keyword">private</a>
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<a id="572" class="Keyword">variable</a>
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<a id="585" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#585" class="Generalizable">o</a> <a id="587" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#587" class="Generalizable">ℓ</a> <a id="589" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#589" class="Generalizable">e</a> <a id="591" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#591" class="Generalizable">o′</a> <a id="594" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#594" class="Generalizable">ℓ′</a> <a id="597" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#597" class="Generalizable">e′</a> <a id="600" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#600" class="Generalizable">o″</a> <a id="603" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#603" class="Generalizable">ℓ″</a> <a id="606" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#606" class="Generalizable">e″</a> <a id="609" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#609" class="Generalizable">o‴</a> <a id="612" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#612" class="Generalizable">ℓ‴</a> <a id="615" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#615" class="Generalizable">e‴</a> <a id="618" class="Symbol">:</a> <a id="620" href="Agda.Primitive.html#591" class="Postulate">Level</a>
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<a id="627" class="Keyword">open</a> <a id="632" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="641" class="Keyword">using</a> <a id="647" class="Symbol">(</a><a id="648" href="Categories.Category.Core.html#559" class="Field">Obj</a><a id="651" class="Symbol">;</a> <a id="653" href="Categories.Category.Core.html#630" class="Field">id</a><a id="655" class="Symbol">)</a>
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<a id="658" class="Comment">-- Functor identity laws lifted to heterogeneous identities.</a>
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<a id="hid-identity"></a><a id="720" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#720" class="Function">hid-identity</a> <a id="733" class="Symbol">:</a> <a id="735" class="Symbol">(</a><a id="736" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#736" class="Bound">C</a> <a id="738" class="Symbol">:</a> <a id="740" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="749" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#585" class="Generalizable">o</a> <a id="751" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#587" class="Generalizable">ℓ</a> <a id="753" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#589" class="Generalizable">e</a><a id="754" class="Symbol">)</a> <a id="756" class="Symbol">(</a><a id="757" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#757" class="Bound">D</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.Morphism.HeterogeneousIdentity.Properties.html#591" class="Generalizable">o′</a> <a id="773" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#594" class="Generalizable">ℓ′</a> <a id="776" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#597" class="Generalizable">e′</a><a id="778" class="Symbol">)</a>
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<a id="795" class="Symbol">{</a><a id="796" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#796" class="Bound">F₀</a> <a id="799" class="Symbol">:</a> <a id="801" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="805" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#736" class="Bound">C</a> <a id="807" class="Symbol">→</a> <a id="809" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="813" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#757" class="Bound">D</a><a id="814" class="Symbol">}</a>
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<a id="831" class="Symbol">(</a><a id="832" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#832" class="Bound">F₁</a> <a id="835" class="Symbol">:</a> <a id="837" class="Symbol">∀</a> <a id="839" class="Symbol">{</a><a id="840" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#840" class="Bound">A</a> <a id="842" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#842" class="Bound">B</a><a id="843" class="Symbol">}</a> <a id="845" class="Symbol">→</a> <a id="847" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#736" class="Bound">C</a> <a id="849" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="851" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#840" class="Bound">A</a> <a id="853" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="855" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#842" class="Bound">B</a> <a id="857" href="Categories.Category.html#502" class="Function Operator">]</a> <a id="859" class="Symbol">→</a> <a id="861" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#757" class="Bound">D</a> <a id="863" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="865" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#796" class="Bound">F₀</a> <a id="868" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#840" class="Bound">A</a> <a id="870" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="872" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#796" class="Bound">F₀</a> <a id="875" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#842" class="Bound">B</a> <a id="877" href="Categories.Category.html#502" class="Function Operator">]</a><a id="878" class="Symbol">)</a> <a id="880" class="Symbol">→</a>
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<a id="897" class="Symbol">(∀</a> <a id="900" class="Symbol">{</a><a id="901" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#901" class="Bound">A</a><a id="902" class="Symbol">}</a> <a id="904" class="Symbol">→</a> <a id="906" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#757" class="Bound">D</a> <a id="908" href="Categories.Category.html#609" class="Function Operator">[</a> <a id="910" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#832" class="Bound">F₁</a> <a id="913" class="Symbol">(</a><a id="914" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="917" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#736" class="Bound">C</a> <a id="919" class="Symbol">{</a><a id="920" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#901" class="Bound">A</a><a id="921" class="Symbol">})</a> <a id="924" href="Categories.Category.html#609" class="Function Operator">≈</a> <a id="926" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="929" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#757" class="Bound">D</a> <a id="931" href="Categories.Category.html#609" class="Function Operator">]</a><a id="932" class="Symbol">)</a> <a id="934" class="Symbol">→</a>
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<a id="951" class="Symbol">∀</a> <a id="953" class="Symbol">{</a><a id="954" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#954" class="Bound">A</a> <a id="956" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#956" class="Bound">B</a><a id="957" class="Symbol">}</a> <a id="959" class="Symbol">(</a><a id="960" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#960" class="Bound">p</a> <a id="962" class="Symbol">:</a> <a id="964" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#954" class="Bound">A</a> <a id="966" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">≡</a> <a id="968" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#956" class="Bound">B</a><a id="969" class="Symbol">)</a> <a id="971" class="Symbol">→</a> <a id="973" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#757" class="Bound">D</a> <a id="975" href="Categories.Category.html#609" class="Function Operator">[</a> <a id="977" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#832" class="Bound">F₁</a> <a id="980" class="Symbol">(</a><a id="981" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="985" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#736" class="Bound">C</a> <a id="987" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#960" class="Bound">p</a><a id="988" class="Symbol">)</a> <a id="990" href="Categories.Category.html#609" class="Function Operator">≈</a> <a id="992" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="996" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#757" class="Bound">D</a> <a id="998" class="Symbol">(</a><a id="999" href="Relation.Binary.PropositionalEquality.Core.html#1139" class="Function">cong</a> <a id="1004" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#796" class="Bound">F₀</a> <a id="1007" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#960" class="Bound">p</a><a id="1008" class="Symbol">)</a> <a id="1010" href="Categories.Category.html#609" class="Function Operator">]</a>
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<a id="1012" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#720" class="Function">hid-identity</a> <a id="1025" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1025" class="Bound">C</a> <a id="1027" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1027" class="Bound">D</a> <a id="1029" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1029" class="Bound">F₁</a> <a id="1032" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1032" class="Bound">hyp</a> <a id="1036" href="Agda.Builtin.Equality.html#190" class="InductiveConstructor">refl</a> <a id="1041" class="Symbol">=</a> <a id="1043" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1032" class="Bound">hyp</a>
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<a id="hid-identity₂"></a><a id="1048" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1048" class="Function">hid-identity₂</a> <a id="1062" class="Symbol">:</a> <a id="1064" class="Symbol">(</a><a id="1065" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1065" class="Bound">C₁</a> <a id="1068" class="Symbol">:</a> <a id="1070" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="1079" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#585" class="Generalizable">o</a> <a id="1081" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#587" class="Generalizable">ℓ</a> <a id="1083" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#589" class="Generalizable">e</a><a id="1084" class="Symbol">)</a> <a id="1086" class="Symbol">(</a><a id="1087" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1087" class="Bound">C₂</a> <a id="1090" class="Symbol">:</a> <a id="1092" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="1101" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#591" class="Generalizable">o′</a> <a id="1104" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#594" class="Generalizable">ℓ′</a> <a id="1107" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#597" class="Generalizable">e′</a><a id="1109" class="Symbol">)</a>
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<a id="1127" class="Symbol">(</a><a id="1128" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1128" class="Bound">D</a> <a id="1130" class="Symbol">:</a> <a id="1132" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="1141" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#600" class="Generalizable">o″</a> <a id="1144" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#603" class="Generalizable">ℓ″</a> <a id="1147" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#606" class="Generalizable">e″</a><a id="1149" class="Symbol">)</a>
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<a id="1167" class="Symbol">{</a><a id="1168" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1168" class="Bound">F₀</a> <a id="1171" class="Symbol">:</a> <a id="1173" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="1177" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1065" class="Bound">C₁</a> <a id="1180" class="Symbol">→</a> <a id="1182" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="1186" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1087" class="Bound">C₂</a> <a id="1189" class="Symbol">→</a> <a id="1191" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="1195" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1128" class="Bound">D</a><a id="1196" class="Symbol">}</a>
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<a id="1214" class="Symbol">(</a><a id="1215" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1215" class="Bound">F₁</a> <a id="1218" class="Symbol">:</a> <a id="1220" class="Symbol">∀</a> <a id="1222" class="Symbol">{</a><a id="1223" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1223" class="Bound">A₁</a> <a id="1226" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1226" class="Bound">A₂</a> <a id="1229" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1229" class="Bound">B₁</a> <a id="1232" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1232" class="Bound">B₂</a><a id="1234" class="Symbol">}</a> <a id="1236" class="Symbol">→</a> <a id="1238" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1065" class="Bound">C₁</a> <a id="1241" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="1243" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1223" class="Bound">A₁</a> <a id="1246" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="1248" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1229" class="Bound">B₁</a> <a id="1251" href="Categories.Category.html#502" class="Function Operator">]</a> <a id="1253" class="Symbol">→</a> <a id="1255" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1087" class="Bound">C₂</a> <a id="1258" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="1260" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1226" class="Bound">A₂</a> <a id="1263" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="1265" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1232" class="Bound">B₂</a> <a id="1268" href="Categories.Category.html#502" class="Function Operator">]</a> <a id="1270" class="Symbol">→</a>
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<a id="1294" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1128" class="Bound">D</a> <a id="1296" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="1298" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1168" class="Bound">F₀</a> <a id="1301" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1223" class="Bound">A₁</a> <a id="1304" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1226" class="Bound">A₂</a> <a id="1307" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="1309" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1168" class="Bound">F₀</a> <a id="1312" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1229" class="Bound">B₁</a> <a id="1315" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1232" class="Bound">B₂</a> <a id="1318" href="Categories.Category.html#502" class="Function Operator">]</a><a id="1319" class="Symbol">)</a> <a id="1321" class="Symbol">→</a>
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<a id="1339" class="Symbol">(∀</a> <a id="1342" class="Symbol">{</a><a id="1343" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1343" class="Bound">A₁</a> <a id="1346" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1346" class="Bound">A₂</a><a id="1348" class="Symbol">}</a> <a id="1350" class="Symbol">→</a> <a id="1352" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1128" class="Bound">D</a> <a id="1354" href="Categories.Category.html#609" class="Function Operator">[</a> <a id="1356" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1215" class="Bound">F₁</a> <a id="1359" class="Symbol">(</a><a id="1360" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1363" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1065" class="Bound">C₁</a> <a id="1366" class="Symbol">{</a><a id="1367" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1343" class="Bound">A₁</a><a id="1369" class="Symbol">})</a> <a id="1372" class="Symbol">(</a><a id="1373" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1376" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1087" class="Bound">C₂</a> <a id="1379" class="Symbol">{</a><a id="1380" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1346" class="Bound">A₂</a><a id="1382" class="Symbol">})</a> <a id="1385" href="Categories.Category.html#609" class="Function Operator">≈</a> <a id="1387" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1390" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1128" class="Bound">D</a> <a id="1392" href="Categories.Category.html#609" class="Function Operator">]</a><a id="1393" class="Symbol">)</a> <a id="1395" class="Symbol">→</a>
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<a id="1413" class="Symbol">∀</a> <a id="1415" class="Symbol">{</a><a id="1416" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1416" class="Bound">A₁</a> <a id="1419" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1419" class="Bound">A₂</a> <a id="1422" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1422" class="Bound">B₁</a> <a id="1425" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1425" class="Bound">B₂</a><a id="1427" class="Symbol">}</a> <a id="1429" class="Symbol">(</a><a id="1430" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1430" class="Bound">p</a> <a id="1432" class="Symbol">:</a> <a id="1434" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1416" class="Bound">A₁</a> <a id="1437" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">≡</a> <a id="1439" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1422" class="Bound">B₁</a><a id="1441" class="Symbol">)</a> <a id="1443" class="Symbol">(</a><a id="1444" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1444" class="Bound">q</a> <a id="1446" class="Symbol">:</a> <a id="1448" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1419" class="Bound">A₂</a> <a id="1451" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">≡</a> <a id="1453" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1425" class="Bound">B₂</a><a id="1455" class="Symbol">)</a> <a id="1457" class="Symbol">→</a>
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<a id="1475" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1128" class="Bound">D</a> <a id="1477" href="Categories.Category.html#609" class="Function Operator">[</a> <a id="1479" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1215" class="Bound">F₁</a> <a id="1482" class="Symbol">(</a><a id="1483" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="1487" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1065" class="Bound">C₁</a> <a id="1490" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1430" class="Bound">p</a><a id="1491" class="Symbol">)</a> <a id="1493" class="Symbol">(</a><a id="1494" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="1498" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1087" class="Bound">C₂</a> <a id="1501" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1444" class="Bound">q</a><a id="1502" class="Symbol">)</a> <a id="1504" href="Categories.Category.html#609" class="Function Operator">≈</a> <a id="1506" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="1510" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1128" class="Bound">D</a> <a id="1512" class="Symbol">(</a><a id="1513" href="Relation.Binary.PropositionalEquality.Core.html#1376" class="Function">cong₂</a> <a id="1519" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1168" class="Bound">F₀</a> <a id="1522" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1430" class="Bound">p</a> <a id="1524" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1444" class="Bound">q</a><a id="1525" class="Symbol">)</a> <a id="1527" href="Categories.Category.html#609" class="Function Operator">]</a>
|
||
<a id="1529" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1048" class="Function">hid-identity₂</a> <a id="1543" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1543" class="Bound">C₁</a> <a id="1546" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1546" class="Bound">C₂</a> <a id="1549" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1549" class="Bound">D</a> <a id="1551" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1551" class="Bound">F₁</a> <a id="1554" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1554" class="Bound">hyp</a> <a id="1558" href="Agda.Builtin.Equality.html#190" class="InductiveConstructor">refl</a> <a id="1563" href="Agda.Builtin.Equality.html#190" class="InductiveConstructor">refl</a> <a id="1568" class="Symbol">=</a> <a id="1570" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1554" class="Bound">hyp</a>
|
||
|
||
<a id="1575" class="Keyword">module</a> <a id="1582" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1582" class="Module">_</a> <a id="1584" class="Symbol">{</a><a id="1585" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1585" class="Bound">C</a> <a id="1587" class="Symbol">:</a> <a id="1589" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="1598" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#585" class="Generalizable">o</a> <a id="1600" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#587" class="Generalizable">ℓ</a> <a id="1602" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#589" class="Generalizable">e</a><a id="1603" class="Symbol">}</a> <a id="1605" class="Symbol">{</a><a id="1606" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1606" class="Bound">D</a> <a id="1608" class="Symbol">:</a> <a id="1610" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="1619" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#591" class="Generalizable">o′</a> <a id="1622" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#594" class="Generalizable">ℓ′</a> <a id="1625" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#597" class="Generalizable">e′</a><a id="1627" class="Symbol">}</a>
|
||
<a id="1638" class="Symbol">(</a><a id="1639" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1639" class="Bound">F</a> <a id="1641" class="Symbol">:</a> <a id="1643" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1651" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1585" class="Bound">C</a> <a id="1653" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1606" class="Bound">D</a><a id="1654" class="Symbol">)</a> <a id="1656" class="Keyword">where</a>
|
||
<a id="1664" class="Keyword">open</a> <a id="1669" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="1678" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1606" class="Bound">D</a>
|
||
<a id="1682" class="Keyword">open</a> <a id="1687" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="1695" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1639" class="Bound">F</a>
|
||
|
||
<a id="1700" class="Comment">-- functors preserve heterogeneous identities</a>
|
||
|
||
<a id="1749" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1749" class="Function">F-hid</a> <a id="1755" class="Symbol">:</a> <a id="1757" class="Symbol">∀</a> <a id="1759" class="Symbol">{</a><a id="1760" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1760" class="Bound">A</a> <a id="1762" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1762" class="Bound">B</a><a id="1763" class="Symbol">}</a> <a id="1765" class="Symbol">(</a><a id="1766" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1766" class="Bound">p</a> <a id="1768" class="Symbol">:</a> <a id="1770" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1760" class="Bound">A</a> <a id="1772" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">≡</a> <a id="1774" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1762" class="Bound">B</a><a id="1775" class="Symbol">)</a> <a id="1777" class="Symbol">→</a> <a id="1779" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="1782" class="Symbol">(</a><a id="1783" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="1787" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1585" class="Bound">C</a> <a id="1789" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1766" class="Bound">p</a><a id="1790" class="Symbol">)</a> <a id="1792" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="1794" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="1798" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1606" class="Bound">D</a> <a id="1800" class="Symbol">(</a><a id="1801" href="Relation.Binary.PropositionalEquality.Core.html#1139" class="Function">cong</a> <a id="1806" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="1809" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1766" class="Bound">p</a><a id="1810" class="Symbol">)</a>
|
||
<a id="1814" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1749" class="Function">F-hid</a> <a id="1820" class="Symbol">=</a> <a id="1822" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#720" class="Function">hid-identity</a> <a id="1835" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1585" class="Bound">C</a> <a id="1837" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1606" class="Bound">D</a> <a id="1839" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="1842" href="Categories.Functor.Core.html#511" class="Field">identity</a>
|
||
|
||
<a id="1852" class="Keyword">module</a> <a id="1859" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1859" class="Module">_</a> <a id="1861" class="Symbol">{</a><a id="1862" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1862" class="Bound">C₁</a> <a id="1865" class="Symbol">:</a> <a id="1867" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="1876" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#585" class="Generalizable">o</a> <a id="1878" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#587" class="Generalizable">ℓ</a> <a id="1880" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#589" class="Generalizable">e</a><a id="1881" class="Symbol">}</a> <a id="1883" class="Symbol">{</a><a id="1884" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1884" class="Bound">C₂</a> <a id="1887" class="Symbol">:</a> <a id="1889" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="1898" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#591" class="Generalizable">o′</a> <a id="1901" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#594" class="Generalizable">ℓ′</a> <a id="1904" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#597" class="Generalizable">e′</a><a id="1906" class="Symbol">}</a>
|
||
<a id="1917" class="Symbol">{</a><a id="1918" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1918" class="Bound">D</a> <a id="1920" class="Symbol">:</a> <a id="1922" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="1931" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#600" class="Generalizable">o″</a> <a id="1934" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#603" class="Generalizable">ℓ″</a> <a id="1937" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#606" class="Generalizable">e″</a><a id="1939" class="Symbol">}</a> <a id="1941" class="Symbol">(</a><a id="1942" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1942" class="Bound">F</a> <a id="1944" class="Symbol">:</a> <a id="1946" href="Categories.Functor.Bifunctor.html#441" class="Function">Bifunctor</a> <a id="1956" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1862" class="Bound">C₁</a> <a id="1959" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1884" class="Bound">C₂</a> <a id="1962" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1918" class="Bound">D</a><a id="1963" class="Symbol">)</a> <a id="1965" class="Keyword">where</a>
|
||
<a id="1973" class="Keyword">open</a> <a id="1978" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="1987" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1918" class="Bound">D</a>
|
||
<a id="1991" class="Keyword">open</a> <a id="1996" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="2004" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1942" class="Bound">F</a>
|
||
|
||
<a id="2009" class="Comment">-- bifunctors preserve heterogeneous identities</a>
|
||
|
||
<a id="2060" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2060" class="Function">BF-hid</a> <a id="2067" class="Symbol">:</a> <a id="2069" class="Symbol">∀</a> <a id="2071" class="Symbol">{</a><a id="2072" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2072" class="Bound">A₁</a> <a id="2075" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2075" class="Bound">A₂</a> <a id="2078" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2078" class="Bound">B₁</a> <a id="2081" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2081" class="Bound">B₂</a><a id="2083" class="Symbol">}</a> <a id="2085" class="Symbol">(</a><a id="2086" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2086" class="Bound">p</a> <a id="2088" class="Symbol">:</a> <a id="2090" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2072" class="Bound">A₁</a> <a id="2093" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">≡</a> <a id="2095" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2078" class="Bound">B₁</a><a id="2097" class="Symbol">)</a> <a id="2099" class="Symbol">(</a><a id="2100" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2100" class="Bound">q</a> <a id="2102" class="Symbol">:</a> <a id="2104" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2075" class="Bound">A₂</a> <a id="2107" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">≡</a> <a id="2109" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2081" class="Bound">B₂</a><a id="2111" class="Symbol">)</a> <a id="2113" class="Symbol">→</a>
|
||
<a id="2126" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="2129" class="Symbol">(</a><a id="2130" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="2134" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1862" class="Bound">C₁</a> <a id="2137" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2086" class="Bound">p</a> <a id="2139" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#236" class="InductiveConstructor Operator">,,</a> <a id="2142" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="2146" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1884" class="Bound">C₂</a> <a id="2149" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2100" class="Bound">q</a><a id="2150" class="Symbol">)</a> <a id="2152" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="2154" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="2158" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1918" class="Bound">D</a> <a id="2160" class="Symbol">(</a><a id="2161" href="Relation.Binary.PropositionalEquality.Core.html#1376" class="Function">cong₂</a> <a id="2167" class="Symbol">(</a><a id="2168" href="Data.Product.html#3274" class="Function">curry</a> <a id="2174" href="Categories.Functor.Core.html#432" class="Field">F₀</a><a id="2176" class="Symbol">)</a> <a id="2178" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2086" class="Bound">p</a> <a id="2180" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2100" class="Bound">q</a><a id="2181" class="Symbol">)</a>
|
||
<a id="2185" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2060" class="Function">BF-hid</a> <a id="2192" class="Symbol">=</a> <a id="2194" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1048" class="Function">hid-identity₂</a> <a id="2208" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1862" class="Bound">C₁</a> <a id="2211" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1884" class="Bound">C₂</a> <a id="2214" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#1918" class="Bound">D</a> <a id="2216" class="Symbol">(</a><a id="2217" href="Data.Product.html#3274" class="Function">curry</a> <a id="2223" href="Categories.Functor.Core.html#455" class="Field">F₁</a><a id="2225" class="Symbol">)</a> <a id="2227" href="Categories.Functor.Core.html#511" class="Field">identity</a>
|
||
|
||
<a id="2237" class="Keyword">module</a> <a id="2244" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2244" class="Module">_</a> <a id="2246" class="Symbol">(</a><a id="2247" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2247" class="Bound">C</a> <a id="2249" class="Symbol">:</a> <a id="2251" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="2260" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#585" class="Generalizable">o</a> <a id="2262" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#587" class="Generalizable">ℓ</a> <a id="2264" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#589" class="Generalizable">e</a><a id="2265" class="Symbol">)</a> <a id="2267" class="Symbol">(</a><a id="2268" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2268" class="Bound">D</a> <a id="2270" class="Symbol">:</a> <a id="2272" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="2281" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#591" class="Generalizable">o′</a> <a id="2284" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#594" class="Generalizable">ℓ′</a> <a id="2287" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#597" class="Generalizable">e′</a><a id="2289" class="Symbol">)</a> <a id="2291" class="Keyword">where</a>
|
||
<a id="2299" class="Keyword">open</a> <a id="2304" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="2313" class="Symbol">(</a><a id="2314" href="Categories.Category.Product.html#745" class="Function">Product</a> <a id="2322" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2247" class="Bound">C</a> <a id="2324" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2268" class="Bound">D</a><a id="2325" class="Symbol">)</a>
|
||
|
||
<a id="2330" class="Comment">-- products preserve heterogeneous identities</a>
|
||
|
||
<a id="2379" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2379" class="Function">×-hid</a> <a id="2385" class="Symbol">:</a> <a id="2387" class="Symbol">∀</a> <a id="2389" class="Symbol">{</a><a id="2390" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2390" class="Bound">A₁</a> <a id="2393" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2393" class="Bound">A₂</a> <a id="2396" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2396" class="Bound">B₁</a> <a id="2399" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2399" class="Bound">B₂</a><a id="2401" class="Symbol">}</a> <a id="2403" class="Symbol">(</a><a id="2404" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2404" class="Bound">p</a> <a id="2406" class="Symbol">:</a> <a id="2408" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2390" class="Bound">A₁</a> <a id="2411" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">≡</a> <a id="2413" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2396" class="Bound">B₁</a><a id="2415" class="Symbol">)</a> <a id="2417" class="Symbol">(</a><a id="2418" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2418" class="Bound">q</a> <a id="2420" class="Symbol">:</a> <a id="2422" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2393" class="Bound">A₂</a> <a id="2425" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">≡</a> <a id="2427" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2399" class="Bound">B₂</a><a id="2429" class="Symbol">)</a> <a id="2431" class="Symbol">→</a>
|
||
<a id="2443" class="Symbol">(</a><a id="2444" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="2448" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2247" class="Bound">C</a> <a id="2450" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2404" class="Bound">p</a> <a id="2452" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#236" class="InductiveConstructor Operator">,,</a> <a id="2455" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="2459" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2268" class="Bound">D</a> <a id="2461" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2418" class="Bound">q</a><a id="2462" class="Symbol">)</a> <a id="2464" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="2466" href="Categories.Morphism.HeterogeneousIdentity.html#1511" class="Function">hid</a> <a id="2470" class="Symbol">(</a><a id="2471" href="Categories.Category.Product.html#745" class="Function">Product</a> <a id="2479" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2247" class="Bound">C</a> <a id="2481" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2268" class="Bound">D</a><a id="2482" class="Symbol">)</a> <a id="2484" class="Symbol">(</a><a id="2485" href="Relation.Binary.PropositionalEquality.Core.html#1376" class="Function">cong₂</a> <a id="2491" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#236" class="InductiveConstructor Operator">_,,_</a> <a id="2496" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2404" class="Bound">p</a> <a id="2498" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2418" class="Bound">q</a><a id="2499" class="Symbol">)</a>
|
||
<a id="2503" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2379" class="Function">×-hid</a> <a id="2509" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2509" class="Bound">p</a> <a id="2511" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2511" class="Bound">q</a> <a id="2513" class="Symbol">=</a> <a id="2515" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2060" class="Function">BF-hid</a> <a id="2522" class="Symbol">{</a><a id="2523" class="Argument">C₁</a> <a id="2526" class="Symbol">=</a> <a id="2528" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2247" class="Bound">C</a><a id="2529" class="Symbol">}</a> <a id="2531" class="Symbol">{</a><a id="2532" class="Argument">C₂</a> <a id="2535" class="Symbol">=</a> <a id="2537" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2268" class="Bound">D</a><a id="2538" class="Symbol">}</a> <a id="2540" class="Symbol">(</a><a id="2541" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#461" class="Function">idF</a> <a id="2545" href="Categories.Category.Product.html#1962" class="Function Operator">⁂</a> <a id="2547" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#461" class="Function">idF</a><a id="2550" class="Symbol">)</a> <a id="2552" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2509" class="Bound">p</a> <a id="2554" href="Categories.Morphism.HeterogeneousIdentity.Properties.html#2511" class="Bound">q</a>
|
||
</pre></body></html> |