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Leon Vatthauer 2bf4655eae
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<html><head><meta charset="utf-8"><title>Categories.Diagram.Duality</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>
<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>
<a id="70" class="Keyword">module</a> <a id="77" href="Categories.Diagram.Duality.html" class="Module">Categories.Diagram.Duality</a> <a id="104" class="Symbol">{</a><a id="105" href="Categories.Diagram.Duality.html#105" class="Bound">o</a> <a id="107" href="Categories.Diagram.Duality.html#107" class="Bound">ℓ</a> <a id="109" href="Categories.Diagram.Duality.html#109" class="Bound">e</a><a id="110" class="Symbol">}</a> <a id="112" class="Symbol">(</a><a id="113" href="Categories.Diagram.Duality.html#113" class="Bound">C</a> <a id="115" class="Symbol">:</a> <a id="117" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="126" href="Categories.Diagram.Duality.html#105" class="Bound">o</a> <a id="128" href="Categories.Diagram.Duality.html#107" class="Bound">ℓ</a> <a id="130" href="Categories.Diagram.Duality.html#109" class="Bound">e</a><a id="131" class="Symbol">)</a> <a id="133" class="Keyword">where</a>
<a id="140" class="Keyword">open</a> <a id="145" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="154" href="Categories.Diagram.Duality.html#113" class="Bound">C</a>
<a id="157" class="Keyword">open</a> <a id="162" class="Keyword">import</a> <a id="169" href="Level.html" class="Module">Level</a>
<a id="175" class="Keyword">open</a> <a id="180" class="Keyword">import</a> <a id="187" href="Function.html" class="Module">Function</a> <a id="196" class="Keyword">using</a> <a id="202" class="Symbol">(</a><a id="203" href="Function.Base.html#1974" class="Function Operator">_$_</a><a id="206" class="Symbol">)</a>
<a id="208" class="Keyword">open</a> <a id="213" class="Keyword">import</a> <a id="220" href="Relation.Binary.PropositionalEquality.html" class="Module">Relation.Binary.PropositionalEquality</a> <a id="258" class="Keyword">using</a> <a id="264" class="Symbol">(</a><a id="265" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">_≡_</a><a id="268" class="Symbol">;</a> <a id="270" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a><a id="274" class="Symbol">)</a>
<a id="277" class="Keyword">open</a> <a id="282" class="Keyword">import</a> <a id="289" href="Categories.Functor.html" class="Module">Categories.Functor</a>
<a id="308" class="Keyword">open</a> <a id="313" class="Keyword">import</a> <a id="320" href="Categories.Functor.Bifunctor.html" class="Module">Categories.Functor.Bifunctor</a>
<a id="349" class="Keyword">open</a> <a id="354" class="Keyword">import</a> <a id="361" href="Categories.NaturalTransformation.Dinatural.html" class="Module">Categories.NaturalTransformation.Dinatural</a>
<a id="405" class="Keyword">open</a> <a id="410" class="Keyword">import</a> <a id="417" href="Categories.Object.Initial.html" class="Module">Categories.Object.Initial</a>
<a id="443" class="Keyword">open</a> <a id="448" class="Keyword">import</a> <a id="455" href="Categories.Object.Terminal.html" class="Module">Categories.Object.Terminal</a>
<a id="482" class="Keyword">open</a> <a id="487" class="Keyword">import</a> <a id="494" href="Categories.Object.Duality.html" class="Module">Categories.Object.Duality</a>
<a id="520" class="Keyword">open</a> <a id="525" class="Keyword">import</a> <a id="532" href="Categories.Diagram.Equalizer.html" class="Module">Categories.Diagram.Equalizer</a> <a id="561" href="Categories.Category.Core.html#3132" class="Function">op</a>
<a id="564" class="Keyword">open</a> <a id="569" class="Keyword">import</a> <a id="576" href="Categories.Diagram.Coequalizer.html" class="Module">Categories.Diagram.Coequalizer</a> <a id="607" href="Categories.Diagram.Duality.html#113" class="Bound">C</a>
<a id="609" class="Keyword">open</a> <a id="614" class="Keyword">import</a> <a id="621" href="Categories.Diagram.Pullback.html" class="Module">Categories.Diagram.Pullback</a> <a id="649" href="Categories.Category.Core.html#3132" class="Function">op</a>
<a id="652" class="Keyword">open</a> <a id="657" class="Keyword">import</a> <a id="664" href="Categories.Diagram.Pushout.html" class="Module">Categories.Diagram.Pushout</a> <a id="691" href="Categories.Diagram.Duality.html#113" class="Bound">C</a>
<a id="693" class="Keyword">open</a> <a id="698" class="Keyword">import</a> <a id="705" href="Categories.Diagram.Cone.html" class="Module">Categories.Diagram.Cone</a> <a id="729" class="Symbol">as</a> <a id="732" class="Module">Cone</a>
<a id="737" class="Keyword">open</a> <a id="742" class="Keyword">import</a> <a id="749" href="Categories.Diagram.Cocone.html" class="Module">Categories.Diagram.Cocone</a> <a id="775" class="Symbol">as</a> <a id="778" class="Module">Cocone</a>
<a id="785" class="Keyword">open</a> <a id="790" class="Keyword">import</a> <a id="797" href="Categories.Diagram.End.html" class="Module">Categories.Diagram.End</a> <a id="820" class="Symbol">as</a> <a id="823" class="Module">End</a>
<a id="827" class="Keyword">open</a> <a id="832" class="Keyword">import</a> <a id="839" href="Categories.Diagram.Coend.html" class="Module">Categories.Diagram.Coend</a> <a id="864" class="Symbol">as</a> <a id="867" class="Module">Coend</a>
<a id="873" class="Keyword">open</a> <a id="878" class="Keyword">import</a> <a id="885" href="Categories.Diagram.Cowedge.html" class="Module">Categories.Diagram.Cowedge</a> <a id="912" class="Symbol">as</a> <a id="915" class="Module">Cowedge</a>
<a id="923" class="Keyword">open</a> <a id="928" class="Keyword">import</a> <a id="935" href="Categories.Diagram.Limit.html" class="Module">Categories.Diagram.Limit</a> <a id="960" class="Symbol">as</a> <a id="963" class="Module">Limit</a>
<a id="969" class="Keyword">open</a> <a id="974" class="Keyword">import</a> <a id="981" href="Categories.Diagram.Colimit.html" class="Module">Categories.Diagram.Colimit</a> <a id="1008" class="Symbol">as</a> <a id="1011" class="Module">Colimit</a>
<a id="1019" class="Keyword">open</a> <a id="1024" class="Keyword">import</a> <a id="1031" href="Categories.Diagram.Wedge.html" class="Module">Categories.Diagram.Wedge</a> <a id="1056" class="Symbol">as</a> <a id="1059" class="Module">Wedge</a>
<a id="1065" class="Keyword">open</a> <a id="1070" class="Keyword">import</a> <a id="1077" href="Categories.Category.Construction.Cocones.html" class="Module">Categories.Category.Construction.Cocones</a> <a id="1118" class="Keyword">using</a> <a id="1124" class="Symbol">(</a><a id="1125" href="Categories.Category.Construction.Cocones.html#731" class="Function">Cocones</a><a id="1132" class="Symbol">)</a>
<a id="1135" class="Keyword">private</a>
<a id="1145" class="Keyword">variable</a>
<a id="1158" href="Categories.Diagram.Duality.html#1158" class="Generalizable">o′</a> <a id="1161" href="Categories.Diagram.Duality.html#1161" class="Generalizable">ℓ′</a> <a id="1164" href="Categories.Diagram.Duality.html#1164" class="Generalizable">e′</a> <a id="1167" class="Symbol">:</a> <a id="1169" href="Agda.Primitive.html#742" class="Postulate">Level</a>
<a id="1179" href="Categories.Diagram.Duality.html#1179" class="Generalizable">D</a> <a id="1181" href="Categories.Diagram.Duality.html#1181" class="Generalizable">J</a> <a id="1183" class="Symbol">:</a> <a id="1185" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="1194" href="Categories.Diagram.Duality.html#1158" class="Generalizable">o′</a> <a id="1197" href="Categories.Diagram.Duality.html#1161" class="Generalizable">ℓ′</a> <a id="1200" href="Categories.Diagram.Duality.html#1164" class="Generalizable">e′</a>
<a id="1207" href="Categories.Diagram.Duality.html#1207" class="Generalizable">A</a> <a id="1209" href="Categories.Diagram.Duality.html#1209" class="Generalizable">B</a> <a id="1211" class="Symbol">:</a> <a id="1213" href="Categories.Category.Core.html#559" class="Field">Obj</a>
<a id="1221" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="1223" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a> <a id="1225" href="Categories.Diagram.Duality.html#1225" class="Generalizable">h</a> <a id="1227" class="Symbol">:</a> <a id="1229" href="Categories.Diagram.Duality.html#1207" class="Generalizable">A</a> <a id="1231" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="1233" href="Categories.Diagram.Duality.html#1209" class="Generalizable">B</a>
<a id="1236" class="Comment">-- note that what would be called</a>
<a id="1270" class="Comment">-- terminal⇒coInitial and initial⇒coTerminal are in</a>
<a id="1322" class="Comment">-- Categories.Object.Duality</a>
<a id="IsCoequalizer⇒IscoEqualizer"></a><a id="1352" href="Categories.Diagram.Duality.html#1352" class="Function">IsCoequalizer⇒IscoEqualizer</a> <a id="1380" class="Symbol">:</a> <a id="1382" href="Categories.Diagram.Coequalizer.html#406" class="Record">IsCoequalizer</a> <a id="1396" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="1398" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a> <a id="1400" href="Categories.Diagram.Duality.html#1225" class="Generalizable">h</a> <a id="1402" class="Symbol">→</a> <a id="1404" href="Categories.Diagram.Equalizer.html#462" class="Record">IsEqualizer</a> <a id="1416" href="Categories.Diagram.Duality.html#1225" class="Generalizable">h</a> <a id="1418" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="1420" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a>
<a id="1423" href="Categories.Diagram.Duality.html#1352" class="Function">IsCoequalizer⇒IscoEqualizer</a> <a id="1451" href="Categories.Diagram.Duality.html#1451" class="Bound">is-coe</a> <a id="1458" class="Symbol">=</a> <a id="1460" class="Keyword">record</a>
<a id="1469" class="Symbol">{</a> <a id="1471" href="Categories.Diagram.Equalizer.html#542" class="Field">equality</a> <a id="1480" class="Symbol">=</a> <a id="1482" href="Categories.Diagram.Coequalizer.html#488" class="Field">equality</a>
<a id="1493" class="Symbol">;</a> <a id="1495" href="Categories.Diagram.Equalizer.html#575" class="Field">equalize</a> <a id="1504" class="Symbol">=</a> <a id="1506" href="Categories.Diagram.Coequalizer.html#523" class="Field">coequalize</a>
<a id="1519" class="Symbol">;</a> <a id="1521" href="Categories.Diagram.Equalizer.html#628" class="Field">universal</a> <a id="1531" class="Symbol">=</a> <a id="1533" href="Categories.Diagram.Coequalizer.html#576" class="Field">universal</a>
<a id="1545" class="Symbol">;</a> <a id="1547" href="Categories.Diagram.Equalizer.html#691" class="Field">unique</a> <a id="1554" class="Symbol">=</a> <a id="1556" href="Categories.Diagram.Coequalizer.html#652" class="Field">unique</a>
<a id="1565" class="Symbol">}</a>
<a id="1569" class="Keyword">where</a> <a id="1575" class="Keyword">open</a> <a id="1580" href="Categories.Diagram.Coequalizer.html#406" class="Module">IsCoequalizer</a> <a id="1594" href="Categories.Diagram.Duality.html#1451" class="Bound">is-coe</a>
<a id="Coequalizer⇒coEqualizer"></a><a id="1602" href="Categories.Diagram.Duality.html#1602" class="Function">Coequalizer⇒coEqualizer</a> <a id="1626" class="Symbol">:</a> <a id="1628" href="Categories.Diagram.Coequalizer.html#1885" class="Record">Coequalizer</a> <a id="1640" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="1642" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a> <a id="1644" class="Symbol">→</a> <a id="1646" href="Categories.Diagram.Equalizer.html#1948" class="Record">Equalizer</a> <a id="1656" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="1658" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a>
<a id="1660" href="Categories.Diagram.Duality.html#1602" class="Function">Coequalizer⇒coEqualizer</a> <a id="1684" href="Categories.Diagram.Duality.html#1684" class="Bound">coe</a> <a id="1688" class="Symbol">=</a> <a id="1690" class="Keyword">record</a>
<a id="1699" class="Symbol">{</a> <a id="1701" href="Categories.Diagram.Equalizer.html#2024" class="Field">arr</a> <a id="1711" class="Symbol">=</a> <a id="1713" href="Categories.Diagram.Coequalizer.html#1963" class="Field">arr</a>
<a id="1719" class="Symbol">;</a> <a id="1721" href="Categories.Diagram.Equalizer.html#2044" class="Field">isEqualizer</a> <a id="1733" class="Symbol">=</a> <a id="1735" href="Categories.Diagram.Duality.html#1352" class="Function">IsCoequalizer⇒IscoEqualizer</a> <a id="1763" href="Categories.Diagram.Coequalizer.html#1983" class="Field">isCoequalizer</a>
<a id="1779" class="Symbol">}</a>
<a id="1783" class="Keyword">where</a> <a id="1789" class="Keyword">open</a> <a id="1794" href="Categories.Diagram.Coequalizer.html#1885" class="Module">Coequalizer</a> <a id="1806" href="Categories.Diagram.Duality.html#1684" class="Bound">coe</a>
<a id="IscoEqualizer⇒IsCoequalizer"></a><a id="1811" href="Categories.Diagram.Duality.html#1811" class="Function">IscoEqualizer⇒IsCoequalizer</a> <a id="1839" class="Symbol">:</a> <a id="1841" href="Categories.Diagram.Equalizer.html#462" class="Record">IsEqualizer</a> <a id="1853" href="Categories.Diagram.Duality.html#1225" class="Generalizable">h</a> <a id="1855" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="1857" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a> <a id="1859" class="Symbol">→</a> <a id="1861" href="Categories.Diagram.Coequalizer.html#406" class="Record">IsCoequalizer</a> <a id="1875" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="1877" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a> <a id="1879" href="Categories.Diagram.Duality.html#1225" class="Generalizable">h</a>
<a id="1881" href="Categories.Diagram.Duality.html#1811" class="Function">IscoEqualizer⇒IsCoequalizer</a> <a id="1909" href="Categories.Diagram.Duality.html#1909" class="Bound">is-eq</a> <a id="1915" class="Symbol">=</a> <a id="1917" class="Keyword">record</a>
<a id="1926" class="Symbol">{</a> <a id="1928" href="Categories.Diagram.Coequalizer.html#488" class="Field">equality</a> <a id="1937" class="Symbol">=</a> <a id="1939" href="Categories.Diagram.Equalizer.html#542" class="Field">equality</a>
<a id="1950" class="Symbol">;</a> <a id="1952" href="Categories.Diagram.Coequalizer.html#523" class="Field">coequalize</a> <a id="1963" class="Symbol">=</a> <a id="1965" href="Categories.Diagram.Equalizer.html#575" class="Field">equalize</a>
<a id="1976" class="Symbol">;</a> <a id="1978" href="Categories.Diagram.Coequalizer.html#576" class="Field">universal</a> <a id="1988" class="Symbol">=</a> <a id="1990" href="Categories.Diagram.Equalizer.html#628" class="Field">universal</a>
<a id="2002" class="Symbol">;</a> <a id="2004" href="Categories.Diagram.Coequalizer.html#652" class="Field">unique</a> <a id="2011" class="Symbol">=</a> <a id="2013" href="Categories.Diagram.Equalizer.html#691" class="Field">unique</a>
<a id="2022" class="Symbol">}</a>
<a id="2026" class="Keyword">where</a> <a id="2032" class="Keyword">open</a> <a id="2037" href="Categories.Diagram.Equalizer.html#462" class="Module">IsEqualizer</a> <a id="2049" href="Categories.Diagram.Duality.html#1909" class="Bound">is-eq</a>
<a id="coEqualizer⇒Coequalizer"></a><a id="2056" href="Categories.Diagram.Duality.html#2056" class="Function">coEqualizer⇒Coequalizer</a> <a id="2080" class="Symbol">:</a> <a id="2082" href="Categories.Diagram.Equalizer.html#1948" class="Record">Equalizer</a> <a id="2092" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="2094" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a> <a id="2096" class="Symbol">→</a> <a id="2098" href="Categories.Diagram.Coequalizer.html#1885" class="Record">Coequalizer</a> <a id="2110" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="2112" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a>
<a id="2114" href="Categories.Diagram.Duality.html#2056" class="Function">coEqualizer⇒Coequalizer</a> <a id="2138" href="Categories.Diagram.Duality.html#2138" class="Bound">e</a> <a id="2140" class="Symbol">=</a> <a id="2142" class="Keyword">record</a>
<a id="2151" class="Symbol">{</a> <a id="2153" href="Categories.Diagram.Coequalizer.html#1963" class="Field">arr</a> <a id="2164" class="Symbol">=</a> <a id="2166" href="Categories.Diagram.Equalizer.html#2024" class="Field">arr</a>
<a id="2172" class="Symbol">;</a> <a id="2174" href="Categories.Diagram.Coequalizer.html#1983" class="Field">isCoequalizer</a> <a id="2188" class="Symbol">=</a> <a id="2190" href="Categories.Diagram.Duality.html#1811" class="Function">IscoEqualizer⇒IsCoequalizer</a> <a id="2218" href="Categories.Diagram.Equalizer.html#2044" class="Field">isEqualizer</a>
<a id="2232" class="Symbol">}</a>
<a id="2236" class="Keyword">where</a> <a id="2242" class="Keyword">open</a> <a id="2247" href="Categories.Diagram.Equalizer.html#1948" class="Module">Equalizer</a> <a id="2257" href="Categories.Diagram.Duality.html#2138" class="Bound">e</a>
<a id="coPullback⇒Pushout"></a><a id="2260" href="Categories.Diagram.Duality.html#2260" class="Function">coPullback⇒Pushout</a> <a id="2279" class="Symbol">:</a> <a id="2281" href="Categories.Diagram.Pullback.html#2029" class="Record">Pullback</a> <a id="2290" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="2292" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a> <a id="2294" class="Symbol">→</a> <a id="2296" href="Categories.Diagram.Pushout.html#403" class="Record">Pushout</a> <a id="2304" href="Categories.Diagram.Duality.html#1221" class="Generalizable">f</a> <a id="2306" href="Categories.Diagram.Duality.html#1223" class="Generalizable">g</a>
<a id="2308" href="Categories.Diagram.Duality.html#2260" class="Function">coPullback⇒Pushout</a> <a id="2327" href="Categories.Diagram.Duality.html#2327" class="Bound">p</a> <a id="2329" class="Symbol">=</a> <a id="2331" class="Keyword">record</a>
<a id="2340" class="Symbol">{</a> <a id="2342" href="Categories.Diagram.Pushout.html#485" class="Field">i₁</a> <a id="2358" class="Symbol">=</a> <a id="2360" href="Categories.Diagram.Pullback.html#2112" class="Field">p₁</a>
<a id="2365" class="Symbol">;</a> <a id="2367" href="Categories.Diagram.Pushout.html#501" class="Field">i₂</a> <a id="2383" class="Symbol">=</a> <a id="2385" href="Categories.Diagram.Pullback.html#2128" class="Field">p₂</a>
<a id="2390" class="Symbol">;</a> <a id="2392" href="Categories.Diagram.Pushout.html#526" class="Field">commute</a> <a id="2408" class="Symbol">=</a> <a id="2410" href="Categories.Diagram.Pullback.html#854" class="Function">commute</a>
<a id="2420" class="Symbol">;</a> <a id="2422" href="Categories.Diagram.Pushout.html#558" class="Field">universal</a> <a id="2438" class="Symbol">=</a> <a id="2440" href="Categories.Diagram.Pullback.html#886" class="Function">universal</a>
<a id="2452" class="Symbol">;</a> <a id="2454" href="Categories.Diagram.Pushout.html#626" class="Field">unique</a> <a id="2470" class="Symbol">=</a> <a id="2472" href="Categories.Diagram.Pullback.html#956" class="Function">unique</a>
<a id="2481" class="Symbol">;</a> <a id="2483" href="Categories.Diagram.Pushout.html#787" class="Field">universal∘i₁≈h₁</a> <a id="2499" class="Symbol">=</a> <a id="2501" href="Categories.Diagram.Pullback.html#1081" class="Function">p₁∘universal≈h₁</a>
<a id="2519" class="Symbol">;</a> <a id="2521" href="Categories.Diagram.Pushout.html#909" class="Field">universal∘i₂≈h₂</a> <a id="2537" class="Symbol">=</a> <a id="2539" href="Categories.Diagram.Pullback.html#1179" class="Function">p₂∘universal≈h₂</a>
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<a id="2561" class="Keyword">where</a> <a id="2567" class="Keyword">open</a> <a id="2572" href="Categories.Diagram.Pullback.html#2029" class="Module">Pullback</a> <a id="2581" href="Categories.Diagram.Duality.html#2327" class="Bound">p</a>
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<a id="5052" href="Categories.Diagram.Duality.html#5052" class="Function">Cowedge⇒coWedge</a> <a id="5068" class="Symbol">:</a> <a id="5070" href="Categories.Diagram.Cowedge.html#596" class="Record">Cowedge</a> <a id="5078" href="Categories.Diagram.Duality.html#4768" class="Bound">F</a> <a id="5080" class="Symbol">→</a> <a id="5082" href="Categories.Diagram.Wedge.html#553" class="Record">Wedge</a> <a id="5088" href="Categories.Diagram.Duality.html#4862" class="Function">Fop</a>
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<a id="6330" href="Categories.Diagram.Duality.html#6204" class="Function">coApex⇔Coapex</a> <a id="6344" class="Symbol">_</a> <a id="6346" class="Symbol">_</a> <a id="6348" class="Symbol">=</a> <a id="6350" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a>
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<a id="6426" href="Categories.Diagram.Duality.html#3494" class="Function">Cocone⇒coCone</a> <a id="6440" class="Symbol">(</a><a id="6441" href="Categories.Diagram.Duality.html#3186" class="Function">coCone⇒Cocone</a> <a id="6455" href="Categories.Diagram.Duality.html#6381" class="Bound">coCone</a><a id="6461" class="Symbol">)</a> <a id="6463" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">≡</a> <a id="6465" href="Categories.Diagram.Duality.html#6381" class="Bound">coCone</a>
<a id="6478" href="Categories.Diagram.Duality.html#6362" class="Function">coCone⇔Cocone</a> <a id="6492" class="Symbol">_</a> <a id="6494" class="Symbol">=</a> <a id="6496" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a>
<a id="6508" href="Categories.Diagram.Duality.html#6508" class="Function">coCone⇒⇔Cocone⇒</a> <a id="6524" class="Symbol">:</a> <a id="6526" class="Symbol">∀</a> <a id="6528" class="Symbol">{</a><a id="6529" href="Categories.Diagram.Duality.html#6529" class="Bound">K</a> <a id="6531" href="Categories.Diagram.Duality.html#6531" class="Bound">K′</a><a id="6533" class="Symbol">}</a> <a id="6535" class="Symbol">→</a> <a id="6537" class="Symbol">(</a><a id="6538" href="Categories.Diagram.Duality.html#6538" class="Bound">coCone⇒</a> <a id="6546" class="Symbol">:</a> <a id="6548" href="Categories.Diagram.Cone.html#660" class="Record">Cone⇒</a> <a id="6554" href="Categories.Diagram.Duality.html#6192" class="Function">Fop</a> <a id="6558" href="Categories.Diagram.Duality.html#6529" class="Bound">K</a> <a id="6560" href="Categories.Diagram.Duality.html#6531" class="Bound">K′</a><a id="6562" class="Symbol">)</a> <a id="6564" class="Symbol">→</a>
<a id="6590" href="Categories.Diagram.Duality.html#3831" class="Function">Cocone⇒⇒coCone⇒</a> <a id="6606" class="Symbol">(</a><a id="6607" href="Categories.Diagram.Duality.html#3633" class="Function">coCone⇒⇒Cocone⇒</a> <a id="6623" href="Categories.Diagram.Duality.html#6538" class="Bound">coCone⇒</a><a id="6630" class="Symbol">)</a> <a id="6632" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">≡</a> <a id="6634" href="Categories.Diagram.Duality.html#6538" class="Bound">coCone⇒</a>
<a id="6648" href="Categories.Diagram.Duality.html#6508" class="Function">coCone⇒⇔Cocone⇒</a> <a id="6664" class="Symbol">_</a> <a id="6666" class="Symbol">=</a> <a id="6668" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a>
<a id="6681" href="Categories.Diagram.Duality.html#6681" class="Function">coLimit⇔Colimit</a> <a id="6697" class="Symbol">:</a> <a id="6699" class="Symbol">∀</a> <a id="6701" class="Symbol">(</a><a id="6702" href="Categories.Diagram.Duality.html#6702" class="Bound">coLimit</a> <a id="6710" class="Symbol">:</a> <a id="6712" href="Categories.Diagram.Limit.html#934" class="Record">Limit</a> <a id="6718" href="Categories.Diagram.Duality.html#6192" class="Function">Fop</a><a id="6721" class="Symbol">)</a> <a id="6723" class="Symbol">→</a>
<a id="6749" href="Categories.Diagram.Duality.html#4402" class="Function">Colimit⇒coLimit</a> <a id="6765" class="Symbol">(</a><a id="6766" href="Categories.Diagram.Duality.html#4031" class="Function">coLimit⇒Colimit</a> <a id="6782" href="Categories.Diagram.Duality.html#6702" class="Bound">coLimit</a><a id="6789" class="Symbol">)</a> <a id="6791" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">≡</a> <a id="6793" href="Categories.Diagram.Duality.html#6702" class="Bound">coLimit</a>
<a id="6807" href="Categories.Diagram.Duality.html#6681" class="Function">coLimit⇔Colimit</a> <a id="6823" class="Symbol">_</a> <a id="6825" class="Symbol">=</a> <a id="6827" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a>
<a id="6838" class="Keyword">module</a> <a id="6845" href="Categories.Diagram.Duality.html#6845" class="Module">_</a> <a id="6847" class="Symbol">{</a><a id="6848" href="Categories.Diagram.Duality.html#6848" class="Bound">F</a> <a id="6850" class="Symbol">:</a> <a id="6852" href="Categories.Functor.Bifunctor.html#441" class="Function">Bifunctor</a> <a id="6862" class="Symbol">(</a><a id="6863" href="Categories.Category.Core.html#3132" class="Function">Category.op</a> <a id="6875" href="Categories.Diagram.Duality.html#1179" class="Generalizable">D</a><a id="6876" class="Symbol">)</a> <a id="6878" href="Categories.Diagram.Duality.html#1179" class="Generalizable">D</a> <a id="6880" href="Categories.Diagram.Duality.html#113" class="Bound">C</a><a id="6881" class="Symbol">}</a> <a id="6883" class="Keyword">where</a>
<a id="6895" class="Keyword">open</a> <a id="6900" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="6908" href="Categories.Diagram.Duality.html#6848" class="Bound">F</a> <a id="6910" class="Keyword">renaming</a> <a id="6919" class="Symbol">(</a><a id="6920" href="Categories.Functor.Core.html#816" class="Function">op</a> <a id="6923" class="Symbol">to</a> <a id="6926" class="Function">Fop</a><a id="6929" class="Symbol">)</a>
<a id="6938" href="Categories.Diagram.Duality.html#6938" class="Function">coWedge⇔Cowedge</a> <a id="6954" class="Symbol">:</a> <a id="6956" class="Symbol">∀</a> <a id="6958" class="Symbol">(</a><a id="6959" href="Categories.Diagram.Duality.html#6959" class="Bound">coWedge</a> <a id="6967" class="Symbol">:</a> <a id="6969" href="Categories.Diagram.Wedge.html#553" class="Record">Wedge</a> <a id="6975" href="Categories.Diagram.Duality.html#6926" class="Function">Fop</a><a id="6978" class="Symbol">)</a> <a id="6980" class="Symbol">→</a>
<a id="7006" href="Categories.Diagram.Duality.html#5052" class="Function">Cowedge⇒coWedge</a> <a id="7022" class="Symbol">(</a><a id="7023" href="Categories.Diagram.Duality.html#4870" class="Function">coWedge⇒Cowedge</a> <a id="7039" href="Categories.Diagram.Duality.html#6959" class="Bound">coWedge</a><a id="7046" class="Symbol">)</a> <a id="7048" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">≡</a> <a id="7050" href="Categories.Diagram.Duality.html#6959" class="Bound">coWedge</a>
<a id="7064" href="Categories.Diagram.Duality.html#6938" class="Function">coWedge⇔Cowedge</a> <a id="7080" class="Symbol">_</a> <a id="7082" class="Symbol">=</a> <a id="7084" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a>
<a id="7097" href="Categories.Diagram.Duality.html#7097" class="Function">coEnd⇔Coend</a> <a id="7109" class="Symbol">:</a> <a id="7111" class="Symbol">∀</a> <a id="7113" class="Symbol">(</a><a id="7114" href="Categories.Diagram.Duality.html#7114" class="Bound">coEnd</a> <a id="7120" class="Symbol">:</a> <a id="7122" href="Categories.Diagram.End.html#485" class="Record">End</a> <a id="7126" href="Categories.Diagram.Duality.html#6926" class="Function">Fop</a><a id="7129" class="Symbol">)</a> <a id="7131" class="Symbol">→</a>
<a id="7153" href="Categories.Diagram.Duality.html#5473" class="Function">Coend⇒coEnd</a> <a id="7165" class="Symbol">(</a><a id="7166" href="Categories.Diagram.Duality.html#5238" class="Function">coEnd⇒Coend</a> <a id="7178" href="Categories.Diagram.Duality.html#7114" class="Bound">coEnd</a><a id="7183" class="Symbol">)</a> <a id="7185" href="Agda.Builtin.Equality.html#150" class="Datatype Operator">≡</a> <a id="7187" href="Categories.Diagram.Duality.html#7114" class="Bound">coEnd</a>
<a id="7199" href="Categories.Diagram.Duality.html#7097" class="Function">coEnd⇔Coend</a> <a id="7211" class="Symbol">_</a> <a id="7213" class="Symbol">=</a> <a id="7215" href="Agda.Builtin.Equality.html#207" class="InductiveConstructor">refl</a>
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