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104 lines
No EOL
28 KiB
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<html><head><meta charset="utf-8"><title>Categories.Category.Construction.Cocones</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Symbol">{-#</a> <a id="5" class="Keyword">OPTIONS</a> <a id="13" class="Pragma">--without-K</a> <a id="25" class="Pragma">--safe</a> <a id="32" class="Symbol">#-}</a>
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<a id="36" class="Keyword">open</a> <a id="41" class="Keyword">import</a> <a id="48" href="Categories.Category.html" class="Module">Categories.Category</a>
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<a id="68" class="Keyword">open</a> <a id="73" class="Keyword">import</a> <a id="80" href="Categories.Functor.html" class="Module">Categories.Functor</a> <a id="99" class="Keyword">hiding</a> <a id="106" class="Symbol">(</a><a id="107" href="Categories.Functor.html#349" class="Function">id</a><a id="109" class="Symbol">)</a>
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<a id="112" class="Comment">-- Also defines the category of cocones "over a Functor F"</a>
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<a id="172" class="Keyword">module</a> <a id="179" href="Categories.Category.Construction.Cocones.html" class="Module">Categories.Category.Construction.Cocones</a>
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<a id="222" class="Symbol">{</a><a id="223" href="Categories.Category.Construction.Cocones.html#223" class="Bound">o</a> <a id="225" href="Categories.Category.Construction.Cocones.html#225" class="Bound">ℓ</a> <a id="227" href="Categories.Category.Construction.Cocones.html#227" class="Bound">e</a><a id="228" class="Symbol">}</a> <a id="230" class="Symbol">{</a><a id="231" href="Categories.Category.Construction.Cocones.html#231" class="Bound">o′</a> <a id="234" href="Categories.Category.Construction.Cocones.html#234" class="Bound">ℓ′</a> <a id="237" href="Categories.Category.Construction.Cocones.html#237" class="Bound">e′</a><a id="239" class="Symbol">}</a> <a id="241" class="Symbol">{</a><a id="242" href="Categories.Category.Construction.Cocones.html#242" class="Bound">C</a> <a id="244" class="Symbol">:</a> <a id="246" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="255" href="Categories.Category.Construction.Cocones.html#223" class="Bound">o</a> <a id="257" href="Categories.Category.Construction.Cocones.html#225" class="Bound">ℓ</a> <a id="259" href="Categories.Category.Construction.Cocones.html#227" class="Bound">e</a><a id="260" class="Symbol">}</a> <a id="262" class="Symbol">{</a><a id="263" href="Categories.Category.Construction.Cocones.html#263" class="Bound">J</a> <a id="265" class="Symbol">:</a> <a id="267" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="276" href="Categories.Category.Construction.Cocones.html#231" class="Bound">o′</a> <a id="279" href="Categories.Category.Construction.Cocones.html#234" class="Bound">ℓ′</a> <a id="282" href="Categories.Category.Construction.Cocones.html#237" class="Bound">e′</a><a id="284" class="Symbol">}</a> <a id="286" class="Symbol">(</a><a id="287" href="Categories.Category.Construction.Cocones.html#287" class="Bound">F</a> <a id="289" class="Symbol">:</a> <a id="291" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="299" href="Categories.Category.Construction.Cocones.html#263" class="Bound">J</a> <a id="301" href="Categories.Category.Construction.Cocones.html#242" class="Bound">C</a><a id="302" class="Symbol">)</a> <a id="304" class="Keyword">where</a>
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<a id="311" class="Keyword">open</a> <a id="316" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="325" href="Categories.Category.Construction.Cocones.html#242" class="Bound">C</a>
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<a id="328" class="Keyword">private</a>
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<a id="338" class="Keyword">variable</a>
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<a id="351" href="Categories.Category.Construction.Cocones.html#351" class="Generalizable">X</a> <a id="353" class="Symbol">:</a> <a id="355" href="Categories.Category.Core.html#559" class="Function">Obj</a>
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<a id="360" class="Keyword">open</a> <a id="365" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
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<a id="378" class="Keyword">open</a> <a id="383" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="391" href="Categories.Category.Construction.Cocones.html#287" class="Bound">F</a>
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<a id="393" class="Keyword">open</a> <a id="398" class="Keyword">import</a> <a id="405" href="Data.Product.html" class="Module">Data.Product</a>
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<a id="418" class="Keyword">open</a> <a id="423" class="Keyword">import</a> <a id="430" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="446" class="Keyword">using</a> <a id="452" class="Symbol">(</a><a id="453" href="Relation.Binary.Core.html#896" class="Function">Rel</a><a id="456" class="Symbol">;</a> <a id="458" href="Relation.Binary.Structures.html#1550" class="Record">IsEquivalence</a><a id="471" class="Symbol">;</a> <a id="473" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a><a id="479" class="Symbol">)</a>
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<a id="481" class="Keyword">import</a> <a id="488" href="Categories.Morphism.html" class="Module">Categories.Morphism</a> <a id="508" class="Symbol">as</a> <a id="511" class="Module">Mor</a>
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<a id="515" class="Keyword">import</a> <a id="522" href="Categories.Morphism.IsoEquiv.html" class="Module">Categories.Morphism.IsoEquiv</a> <a id="551" class="Symbol">as</a> <a id="554" class="Module">IsoEquiv</a>
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<a id="563" class="Keyword">open</a> <a id="568" class="Keyword">import</a> <a id="575" href="Categories.Diagram.Cocone.html" class="Module">Categories.Diagram.Cocone</a> <a id="601" href="Categories.Category.Construction.Cocones.html#287" class="Bound">F</a> <a id="603" class="Keyword">public</a>
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<a id="611" class="Keyword">open</a> <a id="616" href="Categories.Morphism.html" class="Module">Mor</a> <a id="620" href="Categories.Category.Construction.Cocones.html#242" class="Bound">C</a>
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<a id="622" class="Keyword">open</a> <a id="627" href="Categories.Morphism.IsoEquiv.html" class="Module">IsoEquiv</a> <a id="636" href="Categories.Category.Construction.Cocones.html#242" class="Bound">C</a>
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<a id="638" class="Keyword">open</a> <a id="643" class="Keyword">import</a> <a id="650" href="Categories.Morphism.Reasoning.html" class="Module">Categories.Morphism.Reasoning</a> <a id="680" href="Categories.Category.Construction.Cocones.html#242" class="Bound">C</a>
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<a id="682" class="Keyword">open</a> <a id="687" href="Categories.Diagram.Cocone.html#534" class="Module">Cocone</a>
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<a id="694" class="Keyword">open</a> <a id="699" href="Categories.Diagram.Cocone.html#362" class="Module">Coapex</a>
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<a id="706" class="Keyword">open</a> <a id="711" href="Categories.Diagram.Cocone.html#684" class="Module">Cocone⇒</a>
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<a id="719" class="Keyword">open</a> <a id="724" href="Categories.Category.Core.html#1530" class="Module">Equiv</a>
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<a id="Cocones"></a><a id="731" href="Categories.Category.Construction.Cocones.html#731" class="Function">Cocones</a> <a id="739" class="Symbol">:</a> <a id="741" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="750" class="Symbol">_</a> <a id="752" class="Symbol">_</a> <a id="754" class="Symbol">_</a>
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<a id="756" href="Categories.Category.Construction.Cocones.html#731" class="Function">Cocones</a> <a id="764" class="Symbol">=</a> <a id="766" class="Keyword">record</a>
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<a id="775" class="Symbol">{</a> <a id="777" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="787" class="Symbol">=</a> <a id="789" href="Categories.Diagram.Cocone.html#534" class="Record">Cocone</a>
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<a id="798" class="Symbol">;</a> <a id="800" href="Categories.Category.Core.html#575" class="Field Operator">_⇒_</a> <a id="810" class="Symbol">=</a> <a id="812" href="Categories.Diagram.Cocone.html#684" class="Record">Cocone⇒</a>
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<a id="822" class="Symbol">;</a> <a id="824" href="Categories.Category.Core.html#595" class="Field Operator">_≈_</a> <a id="834" class="Symbol">=</a> <a id="836" class="Symbol">λ</a> <a id="838" href="Categories.Category.Construction.Cocones.html#838" class="Bound">f</a> <a id="840" href="Categories.Category.Construction.Cocones.html#840" class="Bound">g</a> <a id="842" class="Symbol">→</a> <a id="844" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="848" href="Categories.Category.Construction.Cocones.html#838" class="Bound">f</a> <a id="850" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="852" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="856" href="Categories.Category.Construction.Cocones.html#840" class="Bound">g</a>
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<a id="860" class="Symbol">;</a> <a id="862" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="872" class="Symbol">=</a> <a id="874" class="Keyword">record</a> <a id="881" class="Symbol">{</a> <a id="883" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="887" class="Symbol">=</a> <a id="889" href="Categories.Category.Core.html#630" class="Function">id</a> <a id="892" class="Symbol">;</a> <a id="894" href="Categories.Diagram.Cocone.html#770" class="Field">commute</a> <a id="902" class="Symbol">=</a> <a id="904" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a> <a id="914" class="Symbol">}</a>
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<a id="918" class="Symbol">;</a> <a id="920" href="Categories.Category.Core.html#656" class="Field Operator">_∘_</a> <a id="930" class="Symbol">=</a> <a id="932" class="Symbol">λ</a> <a id="934" class="Symbol">{</a><a id="935" href="Categories.Category.Construction.Cocones.html#935" class="Bound">A</a> <a id="937" href="Categories.Category.Construction.Cocones.html#937" class="Bound">B</a> <a id="939" href="Categories.Category.Construction.Cocones.html#939" class="Bound">C</a><a id="940" class="Symbol">}</a> <a id="942" href="Categories.Category.Construction.Cocones.html#942" class="Bound">f</a> <a id="944" href="Categories.Category.Construction.Cocones.html#944" class="Bound">g</a> <a id="946" class="Symbol">→</a> <a id="948" class="Keyword">record</a>
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<a id="959" class="Symbol">{</a> <a id="961" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="969" class="Symbol">=</a> <a id="971" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="975" href="Categories.Category.Construction.Cocones.html#942" class="Bound">f</a> <a id="977" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="979" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="983" href="Categories.Category.Construction.Cocones.html#944" class="Bound">g</a>
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<a id="989" class="Symbol">;</a> <a id="991" href="Categories.Diagram.Cocone.html#770" class="Field">commute</a> <a id="999" class="Symbol">=</a> <a id="1001" class="Symbol">λ</a> <a id="1003" class="Symbol">{</a><a id="1004" href="Categories.Category.Construction.Cocones.html#1004" class="Bound">X</a><a id="1005" class="Symbol">}</a> <a id="1007" class="Symbol">→</a> <a id="1009" href="Relation.Binary.Reasoning.Syntax.html#1510" class="Function Operator">begin</a>
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<a id="1021" class="Symbol">(</a><a id="1022" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="1026" href="Categories.Category.Construction.Cocones.html#942" class="Bound">f</a> <a id="1028" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1030" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="1034" href="Categories.Category.Construction.Cocones.html#944" class="Bound">g</a><a id="1035" class="Symbol">)</a> <a id="1037" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1039" href="Categories.Diagram.Cocone.html#425" class="Field">ψ</a> <a id="1041" href="Categories.Category.Construction.Cocones.html#935" class="Bound">A</a> <a id="1043" href="Categories.Category.Construction.Cocones.html#1004" class="Bound">X</a> <a id="1045" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="1048" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="1054" class="Symbol">(</a><a id="1055" href="Categories.Diagram.Cocone.html#770" class="Field">commute</a> <a id="1063" href="Categories.Category.Construction.Cocones.html#944" class="Bound">g</a><a id="1064" class="Symbol">)</a> <a id="1066" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="1074" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="1078" href="Categories.Category.Construction.Cocones.html#942" class="Bound">f</a> <a id="1080" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1082" href="Categories.Diagram.Cocone.html#425" class="Field">ψ</a> <a id="1084" href="Categories.Category.Construction.Cocones.html#937" class="Bound">B</a> <a id="1086" href="Categories.Category.Construction.Cocones.html#1004" class="Bound">X</a> <a id="1098" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="1101" href="Categories.Diagram.Cocone.html#770" class="Field">commute</a> <a id="1109" href="Categories.Category.Construction.Cocones.html#942" class="Bound">f</a> <a id="1111" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="1119" href="Categories.Diagram.Cocone.html#425" class="Field">ψ</a> <a id="1121" href="Categories.Category.Construction.Cocones.html#939" class="Bound">C</a> <a id="1123" href="Categories.Category.Construction.Cocones.html#1004" class="Bound">X</a> <a id="1143" href="Relation.Binary.Reasoning.Syntax.html#12283" class="Function Operator">∎</a>
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<a id="1149" class="Symbol">}</a>
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<a id="1153" class="Symbol">;</a> <a id="1155" href="Categories.Category.Core.html#715" class="Field">assoc</a> <a id="1165" class="Symbol">=</a> <a id="1167" href="Categories.Category.Core.html#715" class="Function">assoc</a>
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<a id="1175" class="Symbol">;</a> <a id="1177" href="Categories.Category.Core.html#1004" class="Field">sym-assoc</a> <a id="1187" class="Symbol">=</a> <a id="1189" href="Categories.Category.Core.html#1004" class="Function">sym-assoc</a>
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<a id="1201" class="Symbol">;</a> <a id="1203" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="1213" class="Symbol">=</a> <a id="1215" href="Categories.Category.Core.html#1096" class="Function">identityˡ</a>
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<a id="1227" class="Symbol">;</a> <a id="1229" href="Categories.Category.Core.html#1145" class="Field">identityʳ</a> <a id="1239" class="Symbol">=</a> <a id="1241" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a>
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<a id="1253" class="Symbol">;</a> <a id="1255" href="Categories.Category.Core.html#1339" class="Field">identity²</a> <a id="1265" class="Symbol">=</a> <a id="1267" href="Categories.Category.Core.html#1339" class="Function">identity²</a>
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<a id="1279" class="Symbol">;</a> <a id="1281" href="Categories.Category.Core.html#1384" class="Field">equiv</a> <a id="1291" class="Symbol">=</a> <a id="1293" class="Keyword">record</a>
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||
<a id="1304" class="Symbol">{</a> <a id="1306" href="Relation.Binary.Structures.html#1596" class="Field">refl</a> <a id="1312" class="Symbol">=</a> <a id="1314" href="Relation.Binary.Structures.html#1596" class="Function">refl</a>
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||
<a id="1323" class="Symbol">;</a> <a id="1325" href="Relation.Binary.Structures.html#1622" class="Field">sym</a> <a id="1331" class="Symbol">=</a> <a id="1333" href="Relation.Binary.Structures.html#1622" class="Function">sym</a>
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||
<a id="1341" class="Symbol">;</a> <a id="1343" href="Relation.Binary.Structures.html#1648" class="Field">trans</a> <a id="1349" class="Symbol">=</a> <a id="1351" href="Relation.Binary.Structures.html#1648" class="Function">trans</a>
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<a id="1361" class="Symbol">}</a>
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||
<a id="1365" class="Symbol">;</a> <a id="1367" href="Categories.Category.Core.html#1438" class="Field">∘-resp-≈</a> <a id="1377" class="Symbol">=</a> <a id="1379" href="Categories.Category.Core.html#1438" class="Function">∘-resp-≈</a>
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<a id="1390" class="Symbol">}</a>
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<a id="1393" class="Keyword">module</a> <a id="Cocones"></a><a id="1400" href="Categories.Category.Construction.Cocones.html#1400" class="Module">Cocones</a> <a id="1408" class="Symbol">=</a> <a id="1410" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="1419" href="Categories.Category.Construction.Cocones.html#731" class="Function">Cocones</a>
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<a id="1428" class="Keyword">private</a>
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<a id="1438" class="Keyword">variable</a>
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||
<a id="1451" href="Categories.Category.Construction.Cocones.html#1451" class="Generalizable">K</a> <a id="1453" href="Categories.Category.Construction.Cocones.html#1453" class="Generalizable">K′</a> <a id="1456" class="Symbol">:</a> <a id="1458" href="Categories.Diagram.Cocone.html#534" class="Record">Cocone</a>
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||
<a id="1467" class="Keyword">module</a> <a id="CM"></a><a id="1474" href="Categories.Category.Construction.Cocones.html#1474" class="Module">CM</a> <a id="1477" class="Symbol">=</a> <a id="1479" href="Categories.Morphism.html" class="Module">Mor</a> <a id="1483" href="Categories.Category.Construction.Cocones.html#731" class="Function">Cocones</a>
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||
<a id="1493" class="Keyword">module</a> <a id="CI"></a><a id="1500" href="Categories.Category.Construction.Cocones.html#1500" class="Module">CI</a> <a id="1503" class="Symbol">=</a> <a id="1505" href="Categories.Morphism.IsoEquiv.html" class="Module">IsoEquiv</a> <a id="1514" href="Categories.Category.Construction.Cocones.html#731" class="Function">Cocones</a>
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||
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||
<a id="1523" class="Keyword">open</a> <a id="1528" href="Categories.Category.Construction.Cocones.html#1474" class="Module">CM</a> <a id="1531" class="Keyword">using</a> <a id="1537" class="Symbol">()</a> <a id="1540" class="Keyword">renaming</a> <a id="1549" class="Symbol">(</a><a id="1550" href="Categories.Morphism.html#1958" class="Record Operator">_≅_</a> <a id="1554" class="Symbol">to</a> <a id="1557" class="Record Operator">_⇔_</a><a id="1560" class="Symbol">)</a>
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||
<a id="1562" class="Keyword">open</a> <a id="1567" href="Categories.Category.Construction.Cocones.html#1500" class="Module">CI</a> <a id="1570" class="Keyword">using</a> <a id="1576" class="Symbol">()</a> <a id="1579" class="Keyword">renaming</a> <a id="1588" class="Symbol">(</a><a id="1589" href="Categories.Morphism.IsoEquiv.html#1761" class="Record Operator">_≃_</a> <a id="1593" class="Symbol">to</a> <a id="1596" class="Record Operator">_↮_</a><a id="1599" class="Symbol">)</a>
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||
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<a id="cocone-resp-iso"></a><a id="1602" href="Categories.Category.Construction.Cocones.html#1602" class="Function">cocone-resp-iso</a> <a id="1618" class="Symbol">:</a> <a id="1620" class="Symbol">∀</a> <a id="1622" class="Symbol">(</a><a id="1623" href="Categories.Category.Construction.Cocones.html#1623" class="Bound">κ</a> <a id="1625" class="Symbol">:</a> <a id="1627" href="Categories.Diagram.Cocone.html#534" class="Record">Cocone</a><a id="1633" class="Symbol">)</a> <a id="1635" class="Symbol">→</a> <a id="1637" href="Categories.Diagram.Cocone.html#588" class="Field">Cocone.N</a> <a id="1646" href="Categories.Category.Construction.Cocones.html#1623" class="Bound">κ</a> <a id="1648" href="Categories.Morphism.html#1958" class="Record Operator">≅</a> <a id="1650" href="Categories.Category.Construction.Cocones.html#351" class="Generalizable">X</a> <a id="1652" class="Symbol">→</a> <a id="1654" href="Data.Product.Base.html#1244" class="Function">Σ[</a> <a id="1657" href="Categories.Category.Construction.Cocones.html#1657" class="Bound">κ′</a> <a id="1660" href="Data.Product.Base.html#1244" class="Function">∈</a> <a id="1662" href="Categories.Diagram.Cocone.html#534" class="Record">Cocone</a> <a id="1669" href="Data.Product.Base.html#1244" class="Function">]</a> <a id="1671" href="Categories.Category.Construction.Cocones.html#1623" class="Bound">κ</a> <a id="1673" href="Categories.Category.Construction.Cocones.html#1557" class="Record Operator">⇔</a> <a id="1675" href="Categories.Category.Construction.Cocones.html#1657" class="Bound">κ′</a>
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||
<a id="1678" href="Categories.Category.Construction.Cocones.html#1602" class="Function">cocone-resp-iso</a> <a id="1694" class="Symbol">{</a><a id="1695" class="Argument">X</a> <a id="1697" class="Symbol">=</a> <a id="1699" href="Categories.Category.Construction.Cocones.html#1699" class="Bound">X</a><a id="1700" class="Symbol">}</a> <a id="1702" href="Categories.Category.Construction.Cocones.html#1702" class="Bound">κ</a> <a id="1704" href="Categories.Category.Construction.Cocones.html#1704" class="Bound">κ≅X</a> <a id="1708" class="Symbol">=</a> <a id="1710" class="Keyword">record</a>
|
||
<a id="1719" class="Symbol">{</a> <a id="1721" href="Categories.Diagram.Cocone.html#604" class="Field">coapex</a> <a id="1728" class="Symbol">=</a> <a id="1730" class="Keyword">record</a>
|
||
<a id="1741" class="Symbol">{</a> <a id="1743" href="Categories.Diagram.Cocone.html#425" class="Field">ψ</a> <a id="1751" class="Symbol">=</a> <a id="1753" class="Symbol">λ</a> <a id="1755" href="Categories.Category.Construction.Cocones.html#1755" class="Bound">Y</a> <a id="1757" class="Symbol">→</a> <a id="1759" href="Categories.Morphism.html#2006" class="Field">from</a> <a id="1764" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1766" href="Categories.Diagram.Cocone.html#425" class="Function">Cocone.ψ</a> <a id="1775" href="Categories.Category.Construction.Cocones.html#1702" class="Bound">κ</a> <a id="1777" href="Categories.Category.Construction.Cocones.html#1755" class="Bound">Y</a>
|
||
<a id="1783" class="Symbol">;</a> <a id="1785" href="Categories.Diagram.Cocone.html#471" class="Field">commute</a> <a id="1793" class="Symbol">=</a> <a id="1795" class="Symbol">λ</a> <a id="1797" href="Categories.Category.Construction.Cocones.html#1797" class="Bound">f</a> <a id="1799" class="Symbol">→</a> <a id="1801" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="1807" class="Symbol">(</a><a id="1808" href="Categories.Diagram.Cocone.html#471" class="Function">Cocone.commute</a> <a id="1823" href="Categories.Category.Construction.Cocones.html#1702" class="Bound">κ</a> <a id="1825" href="Categories.Category.Construction.Cocones.html#1797" class="Bound">f</a><a id="1826" class="Symbol">)</a>
|
||
<a id="1832" class="Symbol">}</a>
|
||
<a id="1836" class="Symbol">}</a> <a id="1838" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1840" class="Keyword">record</a>
|
||
<a id="1849" class="Symbol">{</a> <a id="1851" href="Categories.Morphism.html#2006" class="Field">from</a> <a id="1856" class="Symbol">=</a> <a id="1858" class="Keyword">record</a>
|
||
<a id="1869" class="Symbol">{</a> <a id="1871" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="1879" class="Symbol">=</a> <a id="1881" href="Categories.Morphism.html#2006" class="Field">from</a>
|
||
<a id="1890" class="Symbol">;</a> <a id="1892" href="Categories.Diagram.Cocone.html#770" class="Field">commute</a> <a id="1900" class="Symbol">=</a> <a id="1902" href="Relation.Binary.Structures.html#1596" class="Function">refl</a>
|
||
<a id="1911" class="Symbol">}</a>
|
||
<a id="1915" class="Symbol">;</a> <a id="1917" href="Categories.Morphism.html#2023" class="Field">to</a> <a id="1922" class="Symbol">=</a> <a id="1924" class="Keyword">record</a>
|
||
<a id="1935" class="Symbol">{</a> <a id="1937" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="1945" class="Symbol">=</a> <a id="1947" href="Categories.Morphism.html#2023" class="Field">to</a>
|
||
<a id="1954" class="Symbol">;</a> <a id="1956" href="Categories.Diagram.Cocone.html#770" class="Field">commute</a> <a id="1964" class="Symbol">=</a> <a id="1966" href="Categories.Morphism.Reasoning.Core.html#6851" class="Function">cancelˡ</a> <a id="1974" href="Categories.Morphism.html#1586" class="Function">isoˡ</a>
|
||
<a id="1983" class="Symbol">}</a>
|
||
<a id="1987" class="Symbol">;</a> <a id="1989" href="Categories.Morphism.html#2040" class="Field">iso</a> <a id="1994" class="Symbol">=</a> <a id="1996" class="Keyword">record</a>
|
||
<a id="2007" class="Symbol">{</a> <a id="2009" href="Categories.Morphism.html#1586" class="Field">isoˡ</a> <a id="2017" class="Symbol">=</a> <a id="2019" href="Categories.Morphism.html#1586" class="Function">isoˡ</a>
|
||
<a id="2028" class="Symbol">;</a> <a id="2030" href="Categories.Morphism.html#1612" class="Field">isoʳ</a> <a id="2038" class="Symbol">=</a> <a id="2040" href="Categories.Morphism.html#1612" class="Function">isoʳ</a>
|
||
<a id="2049" class="Symbol">}</a>
|
||
<a id="2053" class="Symbol">}</a>
|
||
<a id="2057" class="Keyword">where</a> <a id="2063" class="Keyword">open</a> <a id="2068" href="Categories.Morphism.html#1958" class="Module Operator">_≅_</a> <a id="2072" href="Categories.Category.Construction.Cocones.html#1704" class="Bound">κ≅X</a>
|
||
<a id="2084" class="Keyword">open</a> <a id="2089" href="Categories.Diagram.Cocone.html#534" class="Module">Cocone</a>
|
||
<a id="2104" class="Keyword">open</a> <a id="2109" href="Categories.Diagram.Cocone.html#362" class="Module">Coapex</a>
|
||
|
||
<a id="iso-cocone⇒iso-coapex"></a><a id="2117" href="Categories.Category.Construction.Cocones.html#2117" class="Function">iso-cocone⇒iso-coapex</a> <a id="2139" class="Symbol">:</a> <a id="2141" href="Categories.Category.Construction.Cocones.html#1451" class="Generalizable">K</a> <a id="2143" href="Categories.Category.Construction.Cocones.html#1557" class="Record Operator">⇔</a> <a id="2145" href="Categories.Category.Construction.Cocones.html#1453" class="Generalizable">K′</a> <a id="2148" class="Symbol">→</a> <a id="2150" href="Categories.Diagram.Cocone.html#588" class="Field">N</a> <a id="2152" href="Categories.Category.Construction.Cocones.html#1451" class="Generalizable">K</a> <a id="2154" href="Categories.Morphism.html#1958" class="Record Operator">≅</a> <a id="2156" href="Categories.Diagram.Cocone.html#588" class="Field">N</a> <a id="2158" href="Categories.Category.Construction.Cocones.html#1453" class="Generalizable">K′</a>
|
||
<a id="2161" href="Categories.Category.Construction.Cocones.html#2117" class="Function">iso-cocone⇒iso-coapex</a> <a id="2183" href="Categories.Category.Construction.Cocones.html#2183" class="Bound">K⇔K′</a> <a id="2188" class="Symbol">=</a> <a id="2190" class="Keyword">record</a>
|
||
<a id="2199" class="Symbol">{</a> <a id="2201" href="Categories.Morphism.html#2006" class="Field">from</a> <a id="2206" class="Symbol">=</a> <a id="2208" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="2212" href="Categories.Morphism.html#2006" class="Field">from</a>
|
||
<a id="2219" class="Symbol">;</a> <a id="2221" href="Categories.Morphism.html#2023" class="Field">to</a> <a id="2226" class="Symbol">=</a> <a id="2228" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="2232" href="Categories.Morphism.html#2023" class="Field">to</a>
|
||
<a id="2237" class="Symbol">;</a> <a id="2239" href="Categories.Morphism.html#2040" class="Field">iso</a> <a id="2244" class="Symbol">=</a> <a id="2246" class="Keyword">record</a>
|
||
<a id="2257" class="Symbol">{</a> <a id="2259" href="Categories.Morphism.html#1586" class="Field">isoˡ</a> <a id="2264" class="Symbol">=</a> <a id="2266" href="Categories.Morphism.html#1586" class="Function">isoˡ</a>
|
||
<a id="2275" class="Symbol">;</a> <a id="2277" href="Categories.Morphism.html#1612" class="Field">isoʳ</a> <a id="2282" class="Symbol">=</a> <a id="2284" href="Categories.Morphism.html#1612" class="Function">isoʳ</a>
|
||
<a id="2293" class="Symbol">}</a>
|
||
<a id="2297" class="Symbol">}</a>
|
||
<a id="2301" class="Keyword">where</a> <a id="2307" class="Keyword">open</a> <a id="2312" href="Categories.Category.Construction.Cocones.html#1557" class="Module Operator">_⇔_</a> <a id="2316" href="Categories.Category.Construction.Cocones.html#2183" class="Bound">K⇔K′</a>
|
||
</pre></body></html> |