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42 lines
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14 KiB
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<html><head><meta charset="utf-8"><title>Categories.Diagram.End</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Symbol">{-#</a> <a id="5" class="Keyword">OPTIONS</a> <a id="13" class="Pragma">--without-K</a> <a id="25" class="Pragma">--safe</a> <a id="32" class="Symbol">#-}</a>
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<a id="37" class="Keyword">open</a> <a id="42" class="Keyword">import</a> <a id="49" href="Categories.Category.html" class="Module">Categories.Category</a>
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<a id="69" class="Keyword">open</a> <a id="74" class="Keyword">import</a> <a id="81" href="Categories.Functor.Bifunctor.html" class="Module">Categories.Functor.Bifunctor</a>
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<a id="111" class="Keyword">module</a> <a id="118" href="Categories.Diagram.End.html" class="Module">Categories.Diagram.End</a> <a id="141" class="Symbol">{</a><a id="142" href="Categories.Diagram.End.html#142" class="Bound">o</a> <a id="144" href="Categories.Diagram.End.html#144" class="Bound">ℓ</a> <a id="146" href="Categories.Diagram.End.html#146" class="Bound">e</a> <a id="148" href="Categories.Diagram.End.html#148" class="Bound">o′</a> <a id="151" href="Categories.Diagram.End.html#151" class="Bound">ℓ′</a> <a id="154" href="Categories.Diagram.End.html#154" class="Bound">e′</a><a id="156" class="Symbol">}</a> <a id="158" class="Symbol">{</a><a id="159" href="Categories.Diagram.End.html#159" class="Bound">C</a> <a id="161" class="Symbol">:</a> <a id="163" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="172" href="Categories.Diagram.End.html#142" class="Bound">o</a> <a id="174" href="Categories.Diagram.End.html#144" class="Bound">ℓ</a> <a id="176" href="Categories.Diagram.End.html#146" class="Bound">e</a><a id="177" class="Symbol">}</a> <a id="179" class="Symbol">{</a><a id="180" href="Categories.Diagram.End.html#180" class="Bound">D</a> <a id="182" class="Symbol">:</a> <a id="184" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="193" href="Categories.Diagram.End.html#148" class="Bound">o′</a> <a id="196" href="Categories.Diagram.End.html#151" class="Bound">ℓ′</a> <a id="199" href="Categories.Diagram.End.html#154" class="Bound">e′</a><a id="201" class="Symbol">}</a>
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<a id="205" class="Symbol">(</a><a id="206" href="Categories.Diagram.End.html#206" class="Bound">F</a> <a id="208" class="Symbol">:</a> <a id="210" href="Categories.Functor.Bifunctor.html#441" class="Function">Bifunctor</a> <a id="220" class="Symbol">(</a><a id="221" href="Categories.Category.Core.html#3132" class="Function">Category.op</a> <a id="233" href="Categories.Diagram.End.html#159" class="Bound">C</a><a id="234" class="Symbol">)</a> <a id="236" href="Categories.Diagram.End.html#159" class="Bound">C</a> <a id="238" href="Categories.Diagram.End.html#180" class="Bound">D</a><a id="239" class="Symbol">)</a> <a id="241" class="Keyword">where</a>
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<a id="248" class="Keyword">private</a>
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<a id="258" class="Keyword">module</a> <a id="D"></a><a id="265" href="Categories.Diagram.End.html#265" class="Module">D</a> <a id="267" class="Symbol">=</a> <a id="269" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="278" href="Categories.Diagram.End.html#180" class="Bound">D</a>
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<a id="282" class="Keyword">open</a> <a id="287" href="Categories.Diagram.End.html#265" class="Module">D</a>
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<a id="291" class="Keyword">open</a> <a id="296" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
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<a id="311" class="Keyword">open</a> <a id="316" href="Categories.Category.Core.html#1530" class="Module">Equiv</a>
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<a id="324" class="Keyword">variable</a>
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<a id="337" href="Categories.Diagram.End.html#337" class="Generalizable">A</a> <a id="339" href="Categories.Diagram.End.html#339" class="Generalizable">B</a> <a id="341" class="Symbol">:</a> <a id="343" href="Categories.Category.Core.html#559" class="Function">Obj</a>
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<a id="351" href="Categories.Diagram.End.html#351" class="Generalizable">f</a> <a id="353" href="Categories.Diagram.End.html#353" class="Generalizable">g</a> <a id="355" class="Symbol">:</a> <a id="357" href="Categories.Diagram.End.html#337" class="Generalizable">A</a> <a id="359" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="361" href="Categories.Diagram.End.html#339" class="Generalizable">B</a>
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<a id="364" class="Keyword">open</a> <a id="369" class="Keyword">import</a> <a id="376" href="Level.html" class="Module">Level</a>
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<a id="383" class="Keyword">open</a> <a id="388" class="Keyword">import</a> <a id="395" href="Categories.Diagram.Wedge.html" class="Module">Categories.Diagram.Wedge</a> <a id="420" href="Categories.Diagram.End.html#206" class="Bound">F</a>
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<a id="422" class="Keyword">open</a> <a id="427" class="Keyword">import</a> <a id="434" href="Categories.NaturalTransformation.Dinatural.html" class="Module">Categories.NaturalTransformation.Dinatural</a>
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<a id="478" class="Keyword">record</a> <a id="End"></a><a id="485" href="Categories.Diagram.End.html#485" class="Record">End</a> <a id="489" class="Symbol">:</a> <a id="491" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="495" class="Symbol">(</a><a id="496" href="Level.html#602" class="Function">levelOfTerm</a> <a id="508" href="Categories.Diagram.End.html#206" class="Bound">F</a><a id="509" class="Symbol">)</a> <a id="511" class="Keyword">where</a>
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<a id="519" class="Keyword">field</a>
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<a id="End.wedge"></a><a id="529" href="Categories.Diagram.End.html#529" class="Field">wedge</a> <a id="535" class="Symbol">:</a> <a id="537" href="Categories.Diagram.Wedge.html#553" class="Record">Wedge</a>
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<a id="546" class="Keyword">module</a> <a id="End.wedge"></a><a id="553" href="Categories.Diagram.End.html#553" class="Module">wedge</a> <a id="559" class="Symbol">=</a> <a id="561" href="Categories.Diagram.Wedge.html#553" class="Module">Wedge</a> <a id="567" href="Categories.Diagram.End.html#529" class="Field">wedge</a>
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<a id="575" class="Keyword">open</a> <a id="580" href="Categories.Diagram.End.html#553" class="Module">wedge</a> <a id="586" class="Keyword">public</a>
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<a id="595" class="Keyword">open</a> <a id="600" href="Categories.Diagram.Wedge.html#553" class="Module">Wedge</a>
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<a id="609" class="Keyword">field</a>
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<a id="End.factor"></a><a id="619" href="Categories.Diagram.End.html#619" class="Field">factor</a> <a id="629" class="Symbol">:</a> <a id="631" class="Symbol">(</a><a id="632" href="Categories.Diagram.End.html#632" class="Bound">W</a> <a id="634" class="Symbol">:</a> <a id="636" href="Categories.Diagram.Wedge.html#553" class="Record">Wedge</a><a id="641" class="Symbol">)</a> <a id="643" class="Symbol">→</a> <a id="645" href="Categories.Diagram.Wedge.html#599" class="Field">E</a> <a id="647" href="Categories.Diagram.End.html#632" class="Bound">W</a> <a id="649" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="651" href="Categories.Diagram.Wedge.html#599" class="Function">wedge.E</a>
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<a id="End.universal"></a><a id="663" href="Categories.Diagram.End.html#663" class="Field">universal</a> <a id="673" class="Symbol">:</a> <a id="675" class="Symbol">∀</a> <a id="677" class="Symbol">{</a><a id="678" href="Categories.Diagram.End.html#678" class="Bound">W</a> <a id="680" class="Symbol">:</a> <a id="682" href="Categories.Diagram.Wedge.html#553" class="Record">Wedge</a><a id="687" class="Symbol">}</a> <a id="689" class="Symbol">{</a><a id="690" href="Categories.Diagram.End.html#690" class="Bound">A</a><a id="691" class="Symbol">}</a> <a id="693" class="Symbol">→</a> <a id="695" href="Categories.NaturalTransformation.Dinatural.html#851" class="Function">wedge.dinatural.α</a> <a id="713" href="Categories.Diagram.End.html#690" class="Bound">A</a> <a id="715" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="717" href="Categories.Diagram.End.html#619" class="Field">factor</a> <a id="724" href="Categories.Diagram.End.html#678" class="Bound">W</a> <a id="726" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="728" href="Categories.NaturalTransformation.Dinatural.html#851" class="Field">dinatural.α</a> <a id="740" href="Categories.Diagram.End.html#678" class="Bound">W</a> <a id="742" href="Categories.Diagram.End.html#690" class="Bound">A</a>
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<a id="End.unique"></a><a id="748" href="Categories.Diagram.End.html#748" class="Field">unique</a> <a id="758" class="Symbol">:</a> <a id="760" class="Symbol">∀</a> <a id="762" class="Symbol">{</a><a id="763" href="Categories.Diagram.End.html#763" class="Bound">W</a> <a id="765" class="Symbol">:</a> <a id="767" href="Categories.Diagram.Wedge.html#553" class="Record">Wedge</a><a id="772" class="Symbol">}</a> <a id="774" class="Symbol">{</a><a id="775" href="Categories.Diagram.End.html#775" class="Bound">g</a> <a id="777" class="Symbol">:</a> <a id="779" href="Categories.Diagram.Wedge.html#599" class="Field">E</a> <a id="781" href="Categories.Diagram.End.html#763" class="Bound">W</a> <a id="783" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="785" href="Categories.Diagram.Wedge.html#599" class="Function">wedge.E</a><a id="792" class="Symbol">}</a> <a id="794" class="Symbol">→</a> <a id="796" class="Symbol">(∀</a> <a id="799" class="Symbol">{</a><a id="800" href="Categories.Diagram.End.html#800" class="Bound">A</a><a id="801" class="Symbol">}</a> <a id="803" class="Symbol">→</a> <a id="805" href="Categories.NaturalTransformation.Dinatural.html#851" class="Function">wedge.dinatural.α</a> <a id="823" href="Categories.Diagram.End.html#800" class="Bound">A</a> <a id="825" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="827" href="Categories.Diagram.End.html#775" class="Bound">g</a> <a id="829" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="831" href="Categories.NaturalTransformation.Dinatural.html#851" class="Field">dinatural.α</a> <a id="843" href="Categories.Diagram.End.html#763" class="Bound">W</a> <a id="845" href="Categories.Diagram.End.html#800" class="Bound">A</a><a id="846" class="Symbol">)</a> <a id="848" class="Symbol">→</a> <a id="850" href="Categories.Diagram.End.html#619" class="Field">factor</a> <a id="857" href="Categories.Diagram.End.html#763" class="Bound">W</a> <a id="859" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="861" href="Categories.Diagram.End.html#775" class="Bound">g</a>
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<a id="End.η-id"></a><a id="866" href="Categories.Diagram.End.html#866" class="Function">η-id</a> <a id="871" class="Symbol">:</a> <a id="873" href="Categories.Diagram.End.html#619" class="Field">factor</a> <a id="880" href="Categories.Diagram.End.html#529" class="Field">wedge</a> <a id="886" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="888" href="Categories.Category.Core.html#630" class="Function">D.id</a>
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<a id="895" href="Categories.Diagram.End.html#866" class="Function">η-id</a> <a id="900" class="Symbol">=</a> <a id="902" href="Categories.Diagram.End.html#748" class="Field">unique</a> <a id="909" href="Categories.Category.Core.html#1145" class="Function">identityʳ</a>
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<a id="End.unique′"></a><a id="922" href="Categories.Diagram.End.html#922" class="Function">unique′</a> <a id="930" class="Symbol">:(∀</a> <a id="934" class="Symbol">{</a><a id="935" href="Categories.Diagram.End.html#935" class="Bound">A</a><a id="936" class="Symbol">}</a> <a id="938" class="Symbol">→</a> <a id="940" href="Categories.NaturalTransformation.Dinatural.html#851" class="Function">wedge.dinatural.α</a> <a id="958" href="Categories.Diagram.End.html#935" class="Bound">A</a> <a id="960" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="962" href="Categories.Diagram.End.html#351" class="Generalizable">f</a> <a id="964" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="966" href="Categories.NaturalTransformation.Dinatural.html#851" class="Function">wedge.dinatural.α</a> <a id="984" href="Categories.Diagram.End.html#935" class="Bound">A</a> <a id="986" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="988" href="Categories.Diagram.End.html#353" class="Generalizable">g</a><a id="989" class="Symbol">)</a> <a id="991" class="Symbol">→</a> <a id="993" href="Categories.Diagram.End.html#351" class="Generalizable">f</a> <a id="995" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="997" href="Categories.Diagram.End.html#353" class="Generalizable">g</a>
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<a id="1001" href="Categories.Diagram.End.html#922" class="Function">unique′</a> <a id="1009" class="Symbol">{</a><a id="1010" class="Argument">f</a> <a id="1012" class="Symbol">=</a> <a id="1014" href="Categories.Diagram.End.html#1014" class="Bound">f</a><a id="1015" class="Symbol">}</a> <a id="1017" class="Symbol">{</a><a id="1018" class="Argument">g</a> <a id="1020" class="Symbol">=</a> <a id="1022" href="Categories.Diagram.End.html#1022" class="Bound">g</a><a id="1023" class="Symbol">}</a> <a id="1025" href="Categories.Diagram.End.html#1025" class="Bound">eq</a> <a id="1028" class="Symbol">=</a> <a id="1030" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="1032" class="Symbol">(</a><a id="1033" href="Categories.Diagram.End.html#748" class="Field">unique</a> <a id="1040" class="Symbol">{</a><a id="1041" class="Argument">W</a> <a id="1043" class="Symbol">=</a> <a id="1045" href="Categories.Diagram.Wedge.html#724" class="Function">Wedge-∘</a> <a id="1053" href="Categories.Diagram.End.html#529" class="Field">wedge</a> <a id="1059" href="Categories.Diagram.End.html#1014" class="Bound">f</a><a id="1060" class="Symbol">}</a> <a id="1062" href="Relation.Binary.Structures.html#1596" class="Function">refl</a><a id="1066" class="Symbol">)</a> <a id="1068" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="1070" href="Categories.Diagram.End.html#748" class="Field">unique</a> <a id="1077" class="Symbol">(</a><a id="1078" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="1080" href="Categories.Diagram.End.html#1025" class="Bound">eq</a><a id="1082" class="Symbol">)</a>
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