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<!DOCTYPE HTML>
<html><head><meta charset="utf-8"><title>Categories.Category.Construction.Comma</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="36" class="Keyword">module</a> <a id="43" href="Categories.Category.Construction.Comma.html" class="Module">Categories.Category.Construction.Comma</a> <a id="82" class="Keyword">where</a>
<a id="89" class="Keyword">open</a> <a id="94" class="Keyword">import</a> <a id="101" href="Data.Product.html" class="Module">Data.Product</a> <a id="114" class="Keyword">using</a> <a id="120" class="Symbol">(</a><a id="121" href="Data.Product.html#1176" class="Function Operator">_×_</a><a id="124" class="Symbol">;</a> <a id="126" href="Data.Product.html#1378" class="Function">∃</a><a id="127" class="Symbol">;</a> <a id="129" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">_,_</a><a id="132" class="Symbol">;</a> <a id="134" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a><a id="139" class="Symbol">;</a> <a id="141" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a><a id="146" class="Symbol">;</a> <a id="148" href="Data.Product.html#3069" class="Function">zip</a><a id="151" class="Symbol">;</a> <a id="153" href="Data.Product.html#2495" class="Function">map</a><a id="156" class="Symbol">)</a>
<a id="158" class="Keyword">open</a> <a id="163" class="Keyword">import</a> <a id="170" href="Level.html" class="Module">Level</a>
<a id="176" class="Keyword">open</a> <a id="181" class="Keyword">import</a> <a id="188" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="204" class="Keyword">using</a> <a id="210" class="Symbol">(</a><a id="211" href="Relation.Binary.Core.html#891" class="Function">Rel</a><a id="214" class="Symbol">)</a>
<a id="217" class="Keyword">open</a> <a id="222" class="Keyword">import</a> <a id="229" href="Categories.Category.Instance.One.html" class="Module">Categories.Category.Instance.One</a>
<a id="262" class="Keyword">open</a> <a id="267" class="Keyword">import</a> <a id="274" href="Categories.Category.html" class="Module">Categories.Category</a> <a id="294" class="Keyword">using</a> <a id="300" class="Symbol">(</a><a id="301" href="Categories.Category.Core.html#442" class="Record">Category</a><a id="309" class="Symbol">;</a> <a id="311" href="Categories.Category.html#502" class="Function Operator">_[_,_]</a><a id="317" class="Symbol">;</a> <a id="319" href="Categories.Category.html#700" class="Function Operator">_[_∘_]</a><a id="325" class="Symbol">;</a> <a id="327" class="Keyword">module</a> <a id="334" href="Categories.Category.html#824" class="Module">Definitions</a><a id="345" class="Symbol">)</a>
<a id="347" class="Keyword">open</a> <a id="352" class="Keyword">import</a> <a id="359" href="Categories.Functor.html" class="Module">Categories.Functor</a> <a id="378" class="Keyword">using</a> <a id="384" class="Symbol">(</a><a id="385" href="Categories.Functor.Core.html#248" class="Record">Functor</a><a id="392" class="Symbol">)</a>
<a id="394" class="Keyword">open</a> <a id="399" class="Keyword">import</a> <a id="406" href="Categories.Functor.Construction.Constant.html" class="Module">Categories.Functor.Construction.Constant</a> <a id="447" class="Keyword">using</a> <a id="453" class="Symbol">(</a><a id="454" href="Categories.Functor.Construction.Constant.html#719" class="Function">const!</a><a id="460" class="Symbol">)</a>
<a id="462" class="Keyword">import</a> <a id="469" href="Categories.Morphism.Reasoning.Core.html" class="Module">Categories.Morphism.Reasoning.Core</a> <a id="504" class="Symbol">as</a> <a id="507" class="Module">MR</a>
<a id="511" class="Keyword">private</a>
<a id="521" class="Keyword">variable</a>
<a id="534" href="Categories.Category.Construction.Comma.html#534" class="Generalizable">o₁</a> <a id="537" href="Categories.Category.Construction.Comma.html#537" class="Generalizable">ℓ₁</a> <a id="540" href="Categories.Category.Construction.Comma.html#540" class="Generalizable">e₁</a> <a id="543" href="Categories.Category.Construction.Comma.html#543" class="Generalizable">o₂</a> <a id="546" href="Categories.Category.Construction.Comma.html#546" class="Generalizable">ℓ₂</a> <a id="549" href="Categories.Category.Construction.Comma.html#549" class="Generalizable">e₂</a> <a id="552" href="Categories.Category.Construction.Comma.html#552" class="Generalizable">o₃</a> <a id="555" href="Categories.Category.Construction.Comma.html#555" class="Generalizable">ℓ₃</a> <a id="558" href="Categories.Category.Construction.Comma.html#558" class="Generalizable">e₃</a> <a id="561" class="Symbol">:</a> <a id="563" href="Agda.Primitive.html#591" class="Postulate">Level</a>
<a id="570" class="Comment">-- things go odd with generalized variables for A B C, use anonymous module instead</a>
<a id="654" class="Keyword">module</a> <a id="661" href="Categories.Category.Construction.Comma.html#661" class="Module">_</a> <a id="663" class="Symbol">{</a><a id="664" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a> <a id="666" class="Symbol">:</a> <a id="668" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="677" href="Categories.Category.Construction.Comma.html#534" class="Generalizable">o₁</a> <a id="680" href="Categories.Category.Construction.Comma.html#537" class="Generalizable">ℓ₁</a> <a id="683" href="Categories.Category.Construction.Comma.html#540" class="Generalizable">e₁</a><a id="685" class="Symbol">}</a> <a id="688" class="Symbol">{</a><a id="689" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a> <a id="691" class="Symbol">:</a> <a id="693" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="702" href="Categories.Category.Construction.Comma.html#543" class="Generalizable">o₂</a> <a id="705" href="Categories.Category.Construction.Comma.html#546" class="Generalizable">ℓ₂</a> <a id="708" href="Categories.Category.Construction.Comma.html#549" class="Generalizable">e₂</a><a id="710" class="Symbol">}</a> <a id="712" class="Symbol">{</a><a id="713" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a> <a id="715" class="Symbol">:</a> <a id="717" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="726" href="Categories.Category.Construction.Comma.html#552" class="Generalizable">o₃</a> <a id="729" href="Categories.Category.Construction.Comma.html#555" class="Generalizable">ℓ₃</a> <a id="732" href="Categories.Category.Construction.Comma.html#558" class="Generalizable">e₃</a><a id="734" class="Symbol">}</a> <a id="736" class="Keyword">where</a>
<a id="744" class="Keyword">private</a>
<a id="756" class="Keyword">module</a> <a id="763" href="Categories.Category.Construction.Comma.html#763" class="Module">C</a> <a id="765" class="Symbol">=</a> <a id="767" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="776" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a>
<a id="782" class="Keyword">module</a> <a id="789" href="Categories.Category.Construction.Comma.html#789" class="Module">A</a> <a id="791" class="Symbol">=</a> <a id="793" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="802" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a>
<a id="808" class="Keyword">module</a> <a id="815" href="Categories.Category.Construction.Comma.html#815" class="Module">B</a> <a id="817" class="Symbol">=</a> <a id="819" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="828" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a>
<a id="833" class="Keyword">record</a> <a id="840" href="Categories.Category.Construction.Comma.html#840" class="Record">CommaObj</a> <a id="849" class="Symbol">(</a><a id="850" href="Categories.Category.Construction.Comma.html#850" class="Bound">T</a> <a id="852" class="Symbol">:</a> <a id="854" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="862" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a> <a id="864" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a><a id="865" class="Symbol">)</a> <a id="867" class="Symbol">(</a><a id="868" href="Categories.Category.Construction.Comma.html#868" class="Bound">S</a> <a id="870" class="Symbol">:</a> <a id="872" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="880" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a> <a id="882" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a><a id="883" class="Symbol">)</a> <a id="885" class="Symbol">:</a> <a id="887" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="891" class="Symbol">(</a><a id="892" href="Categories.Category.Construction.Comma.html#677" class="Bound">o₁</a> <a id="895" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="897" href="Categories.Category.Construction.Comma.html#702" class="Bound">o₂</a> <a id="900" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="902" href="Categories.Category.Construction.Comma.html#729" class="Bound">ℓ₃</a><a id="904" class="Symbol">)</a> <a id="906" class="Keyword">where</a>
<a id="916" class="Keyword">open</a> <a id="921" href="Categories.Category.Core.html#442" class="Module">Category</a>
<a id="934" class="Keyword">open</a> <a id="939" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="947" href="Categories.Category.Construction.Comma.html#850" class="Bound">T</a> <a id="949" class="Keyword">renaming</a> <a id="958" class="Symbol">(</a><a id="959" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="962" class="Symbol">to</a> <a id="965" class="Field">T₀</a><a id="967" class="Symbol">)</a>
<a id="973" class="Keyword">open</a> <a id="978" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="986" href="Categories.Category.Construction.Comma.html#868" class="Bound">S</a> <a id="988" class="Keyword">renaming</a> <a id="997" class="Symbol">(</a><a id="998" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="1001" class="Symbol">to</a> <a id="1004" class="Field">S₀</a><a id="1006" class="Symbol">)</a>
<a id="1012" class="Keyword">field</a>
<a id="1024" class="Symbol">{</a><a id="1025" href="Categories.Category.Construction.Comma.html#1025" class="Field">α</a><a id="1026" class="Symbol">}</a> <a id="1028" class="Symbol">:</a> <a id="1030" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="1034" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a>
<a id="1042" class="Symbol">{</a><a id="1043" href="Categories.Category.Construction.Comma.html#1043" class="Field">β</a><a id="1044" class="Symbol">}</a> <a id="1046" class="Symbol">:</a> <a id="1048" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="1052" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a>
<a id="1060" href="Categories.Category.Construction.Comma.html#1060" class="Field">f</a> <a id="1064" class="Symbol">:</a> <a id="1066" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a> <a id="1068" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="1070" href="Categories.Category.Construction.Comma.html#965" class="Function">T₀</a> <a id="1073" href="Categories.Category.Construction.Comma.html#1025" class="Field">α</a> <a id="1075" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="1077" href="Categories.Category.Construction.Comma.html#1004" class="Function">S₀</a> <a id="1080" href="Categories.Category.Construction.Comma.html#1043" class="Field">β</a> <a id="1082" href="Categories.Category.html#502" class="Function Operator">]</a>
<a id="1087" class="Keyword">record</a> <a id="1094" href="Categories.Category.Construction.Comma.html#1094" class="Record">Comma⇒</a> <a id="1101" class="Symbol">{</a><a id="1102" href="Categories.Category.Construction.Comma.html#1102" class="Bound">T</a> <a id="1104" class="Symbol">:</a> <a id="1106" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1114" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a> <a id="1116" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a><a id="1117" class="Symbol">}</a> <a id="1119" class="Symbol">{</a><a id="1120" href="Categories.Category.Construction.Comma.html#1120" class="Bound">S</a> <a id="1122" class="Symbol">:</a> <a id="1124" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1132" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a> <a id="1134" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a><a id="1135" class="Symbol">}</a> <a id="1137" class="Symbol">(</a><a id="1138" href="Categories.Category.Construction.Comma.html#1138" class="Bound">X₁</a> <a id="1141" href="Categories.Category.Construction.Comma.html#1141" class="Bound">X₂</a> <a id="1144" class="Symbol">:</a> <a id="1146" href="Categories.Category.Construction.Comma.html#840" class="Record">CommaObj</a> <a id="1155" href="Categories.Category.Construction.Comma.html#1102" class="Bound">T</a> <a id="1157" href="Categories.Category.Construction.Comma.html#1120" class="Bound">S</a><a id="1158" class="Symbol">)</a> <a id="1160" class="Symbol">:</a> <a id="1162" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1166" class="Symbol">(</a><a id="1167" href="Categories.Category.Construction.Comma.html#680" class="Bound">ℓ₁</a> <a id="1170" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1172" href="Categories.Category.Construction.Comma.html#705" class="Bound">ℓ₂</a> <a id="1175" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1177" href="Categories.Category.Construction.Comma.html#732" class="Bound">e₃</a><a id="1179" class="Symbol">)</a> <a id="1181" class="Keyword">where</a>
<a id="1191" class="Keyword">open</a> <a id="1196" href="Categories.Category.Construction.Comma.html#840" class="Module">CommaObj</a> <a id="1205" href="Categories.Category.Construction.Comma.html#1138" class="Bound">X₁</a> <a id="1208" class="Keyword">renaming</a> <a id="1217" class="Symbol">(</a><a id="1218" href="Categories.Category.Construction.Comma.html#1025" class="Field">α</a> <a id="1220" class="Symbol">to</a> <a id="1223" class="Field">α₁</a><a id="1225" class="Symbol">;</a> <a id="1227" href="Categories.Category.Construction.Comma.html#1043" class="Field">β</a> <a id="1229" class="Symbol">to</a> <a id="1232" class="Field">β₁</a><a id="1234" class="Symbol">;</a> <a id="1236" href="Categories.Category.Construction.Comma.html#1060" class="Field">f</a> <a id="1238" class="Symbol">to</a> <a id="1241" class="Field">f₁</a><a id="1243" class="Symbol">)</a>
<a id="1249" class="Keyword">open</a> <a id="1254" href="Categories.Category.Construction.Comma.html#840" class="Module">CommaObj</a> <a id="1263" href="Categories.Category.Construction.Comma.html#1141" class="Bound">X₂</a> <a id="1266" class="Keyword">renaming</a> <a id="1275" class="Symbol">(</a><a id="1276" href="Categories.Category.Construction.Comma.html#1025" class="Field">α</a> <a id="1278" class="Symbol">to</a> <a id="1281" class="Field">α₂</a><a id="1283" class="Symbol">;</a> <a id="1285" href="Categories.Category.Construction.Comma.html#1043" class="Field">β</a> <a id="1287" class="Symbol">to</a> <a id="1290" class="Field">β₂</a><a id="1292" class="Symbol">;</a> <a id="1294" href="Categories.Category.Construction.Comma.html#1060" class="Field">f</a> <a id="1296" class="Symbol">to</a> <a id="1299" class="Field">f₂</a><a id="1301" class="Symbol">)</a>
<a id="1307" class="Keyword">open</a> <a id="1312" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="1320" href="Categories.Category.Construction.Comma.html#1102" class="Bound">T</a> <a id="1322" class="Keyword">renaming</a> <a id="1331" class="Symbol">(</a><a id="1332" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="1335" class="Symbol">to</a> <a id="1338" class="Field">T₁</a><a id="1340" class="Symbol">)</a>
<a id="1346" class="Keyword">open</a> <a id="1351" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="1359" href="Categories.Category.Construction.Comma.html#1120" class="Bound">S</a> <a id="1361" class="Keyword">renaming</a> <a id="1370" class="Symbol">(</a><a id="1371" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="1374" class="Symbol">to</a> <a id="1377" class="Field">S₁</a><a id="1379" class="Symbol">)</a>
<a id="1385" class="Keyword">open</a> <a id="1390" href="Categories.Category.html#824" class="Module">Definitions</a> <a id="1402" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a>
<a id="1409" class="Keyword">field</a>
<a id="1421" href="Categories.Category.Construction.Comma.html#1421" class="Field">g</a> <a id="1429" class="Symbol">:</a> <a id="1431" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a> <a id="1433" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="1435" href="Categories.Category.Construction.Comma.html#1223" class="Function">α₁</a> <a id="1438" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="1440" href="Categories.Category.Construction.Comma.html#1281" class="Function">α₂</a> <a id="1443" href="Categories.Category.html#502" class="Function Operator">]</a>
<a id="1451" href="Categories.Category.Construction.Comma.html#1451" class="Field">h</a> <a id="1459" class="Symbol">:</a> <a id="1461" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a> <a id="1463" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="1465" href="Categories.Category.Construction.Comma.html#1232" class="Function">β₁</a> <a id="1468" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="1470" href="Categories.Category.Construction.Comma.html#1290" class="Function">β₂</a> <a id="1473" href="Categories.Category.html#502" class="Function Operator">]</a>
<a id="1481" href="Categories.Category.Construction.Comma.html#1481" class="Field">commute</a> <a id="1489" class="Symbol">:</a> <a id="1491" href="Categories.Category.html#884" class="Function">CommutativeSquare</a> <a id="1509" href="Categories.Category.Construction.Comma.html#1241" class="Function">f₁</a> <a id="1512" class="Symbol">(</a><a id="1513" href="Categories.Category.Construction.Comma.html#1338" class="Function">T₁</a> <a id="1516" href="Categories.Category.Construction.Comma.html#1421" class="Field">g</a><a id="1517" class="Symbol">)</a> <a id="1519" class="Symbol">(</a><a id="1520" href="Categories.Category.Construction.Comma.html#1377" class="Function">S₁</a> <a id="1523" href="Categories.Category.Construction.Comma.html#1451" class="Field">h</a><a id="1524" class="Symbol">)</a> <a id="1526" href="Categories.Category.Construction.Comma.html#1299" class="Function">f₂</a>
<a id="1532" href="Categories.Category.Construction.Comma.html#1532" class="Function">Comma</a> <a id="1538" class="Symbol">:</a> <a id="1540" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1548" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a> <a id="1550" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a> <a id="1552" class="Symbol">→</a> <a id="1554" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1562" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a> <a id="1564" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a> <a id="1566" class="Symbol">→</a> <a id="1568" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="1577" class="Symbol">_</a> <a id="1579" class="Symbol">_</a> <a id="1581" class="Symbol">_</a>
<a id="1585" href="Categories.Category.Construction.Comma.html#1532" class="Function">Comma</a> <a id="1591" href="Categories.Category.Construction.Comma.html#1591" class="Bound">T</a> <a id="1593" href="Categories.Category.Construction.Comma.html#1593" class="Bound">S</a> <a id="1595" class="Symbol">=</a> <a id="1597" class="Keyword">record</a>
<a id="1608" class="Symbol">{</a> <a id="1610" href="Categories.Category.Core.html#559" class="Field">Obj</a> <a id="1622" class="Symbol">=</a> <a id="1624" href="Categories.Category.Construction.Comma.html#840" class="Record">CommaObj</a> <a id="1633" href="Categories.Category.Construction.Comma.html#1591" class="Bound">T</a> <a id="1635" href="Categories.Category.Construction.Comma.html#1593" class="Bound">S</a>
<a id="1641" class="Symbol">;</a> <a id="1643" href="Categories.Category.Core.html#575" class="Field Operator">_⇒_</a> <a id="1655" class="Symbol">=</a> <a id="1657" href="Categories.Category.Construction.Comma.html#1094" class="Record">Comma⇒</a>
<a id="1668" class="Symbol">;</a> <a id="1670" href="Categories.Category.Core.html#595" class="Field Operator">_≈_</a> <a id="1682" class="Symbol">=</a> <a id="1684" class="Symbol">λ</a> <a id="1686" href="Categories.Category.Construction.Comma.html#1686" class="Bound">a₁</a> <a id="1689" href="Categories.Category.Construction.Comma.html#1689" class="Bound">a₂</a> <a id="1692" class="Symbol">→</a> <a id="1694" href="Categories.Category.Construction.Comma.html#1421" class="Field">g</a> <a id="1696" href="Categories.Category.Construction.Comma.html#1686" class="Bound">a₁</a> <a id="1699" href="Categories.Category.Core.html#595" class="Function Operator">A.≈</a> <a id="1703" href="Categories.Category.Construction.Comma.html#1421" class="Field">g</a> <a id="1705" href="Categories.Category.Construction.Comma.html#1689" class="Bound">a₂</a> <a id="1708" href="Data.Product.html#1176" class="Function Operator">×</a> <a id="1710" href="Categories.Category.Construction.Comma.html#1451" class="Field">h</a> <a id="1712" href="Categories.Category.Construction.Comma.html#1686" class="Bound">a₁</a> <a id="1715" href="Categories.Category.Core.html#595" class="Function Operator">B.≈</a> <a id="1719" href="Categories.Category.Construction.Comma.html#1451" class="Field">h</a> <a id="1721" href="Categories.Category.Construction.Comma.html#1689" class="Bound">a₂</a>
<a id="1728" class="Symbol">;</a> <a id="1730" href="Categories.Category.Core.html#656" class="Field Operator">_∘_</a> <a id="1742" class="Symbol">=</a> <a id="1744" href="Categories.Category.Construction.Comma.html#2796" class="Function Operator">_∘′_</a>
<a id="1753" class="Symbol">;</a> <a id="1755" href="Categories.Category.Core.html#630" class="Field">id</a> <a id="1767" class="Symbol">=</a> <a id="1769" class="Keyword">record</a> <a id="1776" class="Symbol">{</a> <a id="1778" href="Categories.Category.Construction.Comma.html#1421" class="Field">g</a> <a id="1780" class="Symbol">=</a> <a id="1782" href="Categories.Category.Core.html#630" class="Function">A.id</a> <a id="1787" class="Symbol">;</a> <a id="1789" href="Categories.Category.Construction.Comma.html#1451" class="Field">h</a> <a id="1791" class="Symbol">=</a> <a id="1793" href="Categories.Category.Core.html#630" class="Function">B.id</a> <a id="1798" class="Symbol">;</a> <a id="1800" href="Categories.Category.Construction.Comma.html#1481" class="Field">commute</a> <a id="1808" class="Symbol">=</a> <a id="1810" href="Categories.Category.Construction.Comma.html#2465" class="Function">id-comm</a> <a id="1818" class="Symbol">}</a>
<a id="1824" class="Symbol">;</a> <a id="1826" href="Categories.Category.Core.html#715" class="Field">assoc</a> <a id="1838" class="Symbol">=</a> <a id="1840" href="Categories.Category.Core.html#715" class="Function">A.assoc</a> <a id="1848" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1850" href="Categories.Category.Core.html#715" class="Function">B.assoc</a>
<a id="1862" class="Symbol">;</a> <a id="1864" href="Categories.Category.Core.html#1004" class="Field">sym-assoc</a> <a id="1876" class="Symbol">=</a> <a id="1878" href="Categories.Category.Core.html#1004" class="Function">A.sym-assoc</a> <a id="1890" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1892" href="Categories.Category.Core.html#1004" class="Function">B.sym-assoc</a>
<a id="1908" class="Symbol">;</a> <a id="1910" href="Categories.Category.Core.html#1096" class="Field">identityˡ</a> <a id="1922" class="Symbol">=</a> <a id="1924" href="Categories.Category.Core.html#1096" class="Function">A.identityˡ</a> <a id="1936" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1938" href="Categories.Category.Core.html#1096" class="Function">B.identityˡ</a>
<a id="1954" class="Symbol">;</a> <a id="1956" href="Categories.Category.Core.html#1145" class="Field">identityʳ</a> <a id="1968" class="Symbol">=</a> <a id="1970" href="Categories.Category.Core.html#1145" class="Function">A.identityʳ</a> <a id="1982" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="1984" href="Categories.Category.Core.html#1145" class="Function">B.identityʳ</a>
<a id="2000" class="Symbol">;</a> <a id="2002" href="Categories.Category.Core.html#1339" class="Field">identity²</a> <a id="2014" class="Symbol">=</a> <a id="2016" href="Categories.Category.Core.html#1339" class="Function">A.identity²</a> <a id="2028" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="2030" href="Categories.Category.Core.html#1339" class="Function">B.identity²</a>
<a id="2046" class="Symbol">;</a> <a id="2048" href="Categories.Category.Core.html#1384" class="Field">equiv</a> <a id="2054" class="Symbol">=</a> <a id="2056" class="Keyword">record</a>
<a id="2069" class="Symbol">{</a> <a id="2071" href="Relation.Binary.Structures.html#1577" class="Field">refl</a> <a id="2077" class="Symbol">=</a> <a id="2079" href="Relation.Binary.Structures.html#1577" class="Function">A.Equiv.refl</a> <a id="2092" href="Agda.Builtin.Sigma.html#218" class="InductiveConstructor Operator">,</a> <a id="2094" href="Relation.Binary.Structures.html#1577" class="Function">B.Equiv.refl</a>
<a id="2113" class="Symbol">;</a> <a id="2115" href="Relation.Binary.Structures.html#1603" class="Field">sym</a> <a id="2121" class="Symbol">=</a> <a id="2123" href="Data.Product.html#2495" class="Function">map</a> <a id="2127" href="Relation.Binary.Structures.html#1603" class="Function">A.Equiv.sym</a> <a id="2139" href="Relation.Binary.Structures.html#1603" class="Function">B.Equiv.sym</a>
<a id="2157" class="Symbol">;</a> <a id="2159" href="Relation.Binary.Structures.html#1629" class="Field">trans</a> <a id="2165" class="Symbol">=</a> <a id="2167" href="Data.Product.html#3069" class="Function">zip</a> <a id="2171" href="Relation.Binary.Structures.html#1629" class="Function">A.Equiv.trans</a> <a id="2185" href="Relation.Binary.Structures.html#1629" class="Function">B.Equiv.trans</a>
<a id="2205" class="Symbol">}</a>
<a id="2211" class="Symbol">;</a> <a id="2213" href="Categories.Category.Core.html#1438" class="Field">∘-resp-≈</a> <a id="2225" class="Symbol">=</a> <a id="2227" href="Data.Product.html#3069" class="Function">zip</a> <a id="2231" href="Categories.Category.Core.html#1438" class="Function">A.∘-resp-≈</a> <a id="2242" href="Categories.Category.Core.html#1438" class="Function">B.∘-resp-≈</a>
<a id="2257" class="Symbol">}</a> <a id="2259" class="Keyword">module</a> <a id="2266" href="Categories.Category.Construction.Comma.html#2266" class="Module">Comma</a>
<a id="2276" class="Keyword">where</a>
<a id="2288" class="Keyword">module</a> <a id="2295" href="Categories.Category.Construction.Comma.html#2295" class="Module">T</a> <a id="2297" class="Symbol">=</a> <a id="2299" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="2307" href="Categories.Category.Construction.Comma.html#1591" class="Bound">T</a>
<a id="2315" class="Keyword">module</a> <a id="2322" href="Categories.Category.Construction.Comma.html#2322" class="Module">S</a> <a id="2324" class="Symbol">=</a> <a id="2326" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="2334" href="Categories.Category.Construction.Comma.html#1593" class="Bound">S</a>
<a id="2343" class="Keyword">open</a> <a id="2348" href="Categories.Category.Construction.Comma.html#2295" class="Module">T</a> <a id="2350" class="Keyword">using</a> <a id="2356" class="Symbol">()</a> <a id="2359" class="Keyword">renaming</a> <a id="2368" class="Symbol">(</a><a id="2369" href="Categories.Functor.Core.html#432" class="Function">F₀</a> <a id="2372" class="Symbol">to</a> <a id="2375" class="Function">T₀</a><a id="2377" class="Symbol">;</a> <a id="2379" href="Categories.Functor.Core.html#455" class="Function">F₁</a> <a id="2382" class="Symbol">to</a> <a id="2385" class="Function">T₁</a><a id="2387" class="Symbol">)</a>
<a id="2395" class="Keyword">open</a> <a id="2400" href="Categories.Category.Construction.Comma.html#2322" class="Module">S</a> <a id="2402" class="Keyword">using</a> <a id="2408" class="Symbol">()</a> <a id="2411" class="Keyword">renaming</a> <a id="2420" class="Symbol">(</a><a id="2421" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="2424" class="Symbol">to</a> <a id="2427" class="Field">S₀</a><a id="2429" class="Symbol">;</a> <a id="2431" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="2434" class="Symbol">to</a> <a id="2437" class="Field">S₁</a><a id="2439" class="Symbol">)</a>
<a id="2447" class="Keyword">open</a> <a id="2452" href="Categories.Category.Construction.Comma.html#1094" class="Module">Comma⇒</a>
<a id="2465" href="Categories.Category.Construction.Comma.html#2465" class="Function">id-comm</a> <a id="2473" class="Symbol">:</a> <a id="2475" class="Symbol">{</a><a id="2476" href="Categories.Category.Construction.Comma.html#2476" class="Bound">E</a> <a id="2478" class="Symbol">:</a> <a id="2480" href="Categories.Category.Construction.Comma.html#840" class="Record">CommaObj</a> <a id="2489" href="Categories.Category.Construction.Comma.html#1591" class="Bound">T</a> <a id="2491" href="Categories.Category.Construction.Comma.html#1593" class="Bound">S</a><a id="2492" class="Symbol">}</a> <a id="2494" class="Symbol">→</a> <a id="2496" class="Keyword">let</a> <a id="2500" class="Keyword">open</a> <a id="2505" href="Categories.Category.Construction.Comma.html#840" class="Module">CommaObj</a> <a id="2514" href="Categories.Category.Construction.Comma.html#2476" class="Bound">E</a> <a id="2516" class="Keyword">in</a>
<a id="2528" href="Categories.Category.Construction.Comma.html#2437" class="Field">S₁</a> <a id="2531" href="Categories.Category.Core.html#630" class="Function">B.id</a> <a id="2536" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="2540" href="Categories.Category.Construction.Comma.html#1060" class="Field">f</a> <a id="2542" href="Categories.Category.Core.html#595" class="Field Operator">C.≈</a> <a id="2546" href="Categories.Category.Construction.Comma.html#1060" class="Field">f</a> <a id="2548" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="2552" href="Categories.Category.Construction.Comma.html#2385" class="Function">T₁</a> <a id="2555" href="Categories.Category.Core.html#630" class="Function">A.id</a>
<a id="2566" href="Categories.Category.Construction.Comma.html#2465" class="Function">id-comm</a> <a id="2574" class="Symbol">{</a><a id="2575" href="Categories.Category.Construction.Comma.html#2575" class="Bound">E</a><a id="2576" class="Symbol">}</a> <a id="2578" class="Symbol">=</a> <a id="2580" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="2594" href="Categories.Category.Construction.Comma.html#2437" class="Field">S₁</a> <a id="2597" href="Categories.Category.Core.html#630" class="Function">B.id</a> <a id="2602" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="2606" href="Categories.Category.Construction.Comma.html#1060" class="Field">f</a> <a id="2608" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="2611" href="Categories.Morphism.Reasoning.Core.html#2948" class="Function">elimˡ</a> <a id="2617" href="Categories.Functor.Core.html#511" class="Field">S.identity</a> <a id="2628" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="2638" href="Categories.Category.Construction.Comma.html#1060" class="Field">f</a> <a id="2652" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="2655" href="Categories.Morphism.Reasoning.Core.html#2899" class="Function">introʳ</a> <a id="2662" href="Categories.Functor.Core.html#511" class="Function">T.identity</a> <a id="2673" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="2683" href="Categories.Category.Construction.Comma.html#1060" class="Field">f</a> <a id="2685" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="2689" href="Categories.Category.Construction.Comma.html#2385" class="Function">T₁</a> <a id="2692" href="Categories.Category.Core.html#630" class="Function">A.id</a> <a id="2697" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="2707" class="Keyword">where</a>
<a id="2723" class="Keyword">open</a> <a id="2728" href="Categories.Category.Core.html#2462" class="Module">C.HomReasoning</a>
<a id="2753" class="Keyword">open</a> <a id="2758" href="Categories.Category.Construction.Comma.html#840" class="Module">CommaObj</a> <a id="2767" href="Categories.Category.Construction.Comma.html#2575" class="Bound">E</a>
<a id="2779" class="Keyword">open</a> <a id="2784" href="Categories.Morphism.Reasoning.Core.html" class="Module">MR</a> <a id="2787" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a>
<a id="2796" href="Categories.Category.Construction.Comma.html#2796" class="Function Operator">_∘′_</a> <a id="2801" class="Symbol">:</a> <a id="2803" class="Symbol">∀</a> <a id="2805" class="Symbol">{</a><a id="2806" href="Categories.Category.Construction.Comma.html#2806" class="Bound">X₁</a> <a id="2809" href="Categories.Category.Construction.Comma.html#2809" class="Bound">X₂</a> <a id="2812" href="Categories.Category.Construction.Comma.html#2812" class="Bound">X₃</a><a id="2814" class="Symbol">}</a> <a id="2816" class="Symbol">→</a> <a id="2818" href="Categories.Category.Construction.Comma.html#1094" class="Record">Comma⇒</a> <a id="2825" href="Categories.Category.Construction.Comma.html#2809" class="Bound">X₂</a> <a id="2828" href="Categories.Category.Construction.Comma.html#2812" class="Bound">X₃</a> <a id="2831" class="Symbol">→</a> <a id="2833" href="Categories.Category.Construction.Comma.html#1094" class="Record">Comma⇒</a> <a id="2840" href="Categories.Category.Construction.Comma.html#2806" class="Bound">X₁</a> <a id="2843" href="Categories.Category.Construction.Comma.html#2809" class="Bound">X₂</a> <a id="2846" class="Symbol">→</a> <a id="2848" href="Categories.Category.Construction.Comma.html#1094" class="Record">Comma⇒</a> <a id="2855" href="Categories.Category.Construction.Comma.html#2806" class="Bound">X₁</a> <a id="2858" href="Categories.Category.Construction.Comma.html#2812" class="Bound">X₃</a>
<a id="2867" href="Categories.Category.Construction.Comma.html#2796" class="Function Operator">_∘′_</a> <a id="2872" class="Symbol">{</a><a id="2873" href="Categories.Category.Construction.Comma.html#2873" class="Bound">X₁</a><a id="2875" class="Symbol">}</a> <a id="2877" class="Symbol">{</a><a id="2878" href="Categories.Category.Construction.Comma.html#2878" class="Bound">X₂</a><a id="2880" class="Symbol">}</a> <a id="2882" class="Symbol">{</a><a id="2883" href="Categories.Category.Construction.Comma.html#2883" class="Bound">X₃</a><a id="2885" class="Symbol">}</a> <a id="2887" href="Categories.Category.Construction.Comma.html#2887" class="Bound">a₁</a> <a id="2890" href="Categories.Category.Construction.Comma.html#2890" class="Bound">a₂</a> <a id="2893" class="Symbol">=</a> <a id="2895" class="Keyword">record</a>
<a id="2910" class="Symbol">{</a> <a id="2912" href="Categories.Category.Construction.Comma.html#1421" class="Field">g</a> <a id="2914" class="Symbol">=</a> <a id="2916" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a> <a id="2918" href="Categories.Category.html#700" class="Function Operator">[</a> <a id="2920" href="Categories.Category.Construction.Comma.html#3321" class="Function">g₁</a> <a id="2923" href="Categories.Category.html#700" class="Function Operator">∘</a> <a id="2925" href="Categories.Category.Construction.Comma.html#3394" class="Field">g₂</a> <a id="2928" href="Categories.Category.html#700" class="Function Operator">]</a>
<a id="2938" class="Symbol">;</a> <a id="2940" href="Categories.Category.Construction.Comma.html#1451" class="Field">h</a> <a id="2942" class="Symbol">=</a> <a id="2944" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a> <a id="2946" href="Categories.Category.html#700" class="Function Operator">[</a> <a id="2948" href="Categories.Category.Construction.Comma.html#3330" class="Function">h₁</a> <a id="2951" href="Categories.Category.html#700" class="Function Operator">∘</a> <a id="2953" href="Categories.Category.Construction.Comma.html#3403" class="Field">h₂</a> <a id="2956" href="Categories.Category.html#700" class="Function Operator">]</a>
<a id="2966" class="Symbol">;</a> <a id="2968" href="Categories.Category.Construction.Comma.html#1481" class="Field">commute</a> <a id="2976" class="Symbol">=</a> <a id="2978" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="2994" href="Categories.Category.Construction.Comma.html#2437" class="Field">S₁</a> <a id="2997" class="Symbol">(</a><a id="2998" href="Categories.Category.Construction.Comma.html#3330" class="Function">h₁</a> <a id="3001" href="Categories.Category.Core.html#656" class="Function Operator">B.∘</a> <a id="3005" href="Categories.Category.Construction.Comma.html#3403" class="Field">h₂</a><a id="3007" class="Symbol">)</a> <a id="3009" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="3013" href="Categories.Category.Construction.Comma.html#3469" class="Function">f₁</a> <a id="3019" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="3022" href="Categories.Functor.Core.html#565" class="Field">S.homomorphism</a> <a id="3037" href="Categories.Category.Core.html#2837" class="Function Operator">⟩∘⟨refl</a> <a id="3045" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="3057" class="Symbol">(</a><a id="3058" href="Categories.Category.Construction.Comma.html#2437" class="Field">S₁</a> <a id="3061" href="Categories.Category.Construction.Comma.html#3330" class="Function">h₁</a> <a id="3064" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="3068" href="Categories.Category.Construction.Comma.html#2437" class="Field">S₁</a> <a id="3071" href="Categories.Category.Construction.Comma.html#3403" class="Field">h₂</a><a id="3073" class="Symbol">)</a> <a id="3075" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="3079" href="Categories.Category.Construction.Comma.html#3469" class="Function">f₁</a> <a id="3082" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="3085" href="Categories.Morphism.Reasoning.Core.html#4290" class="Function">glue</a> <a id="3090" href="Categories.Category.Construction.Comma.html#3345" class="Function">commutes₁</a> <a id="3100" href="Categories.Category.Construction.Comma.html#3418" class="Field">commutes₂</a> <a id="3110" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="3122" href="Categories.Category.Construction.Comma.html#3557" class="Function">f₃</a> <a id="3125" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="3129" class="Symbol">(</a><a id="3130" href="Categories.Category.Construction.Comma.html#2385" class="Function">T₁</a> <a id="3133" href="Categories.Category.Construction.Comma.html#3321" class="Function">g₁</a> <a id="3136" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="3140" href="Categories.Category.Construction.Comma.html#2385" class="Function">T₁</a> <a id="3143" href="Categories.Category.Construction.Comma.html#3394" class="Field">g₂</a><a id="3145" class="Symbol">)</a> <a id="3147" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">≈˘⟨</a> <a id="3151" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="3159" href="Categories.Functor.Core.html#565" class="Function">T.homomorphism</a> <a id="3174" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">⟩</a>
<a id="3186" href="Categories.Category.Construction.Comma.html#3557" class="Function">f₃</a> <a id="3189" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="3193" href="Categories.Category.Construction.Comma.html#2385" class="Function">T₁</a> <a id="3196" class="Symbol">(</a><a id="3197" href="Categories.Category.Construction.Comma.html#3321" class="Function">g₁</a> <a id="3200" href="Categories.Category.Core.html#656" class="Function Operator">A.∘</a> <a id="3204" href="Categories.Category.Construction.Comma.html#3394" class="Field">g₂</a><a id="3206" class="Symbol">)</a> <a id="3211" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
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<a id="3231" class="Keyword">where</a>
<a id="3245" class="Keyword">open</a> <a id="3250" href="Categories.Category.Core.html#2462" class="Module">C.HomReasoning</a>
<a id="3273" class="Keyword">open</a> <a id="3278" href="Categories.Morphism.Reasoning.Core.html" class="Module">MR</a> <a id="3281" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a>
<a id="3291" class="Keyword">open</a> <a id="3296" href="Categories.Category.Construction.Comma.html#1094" class="Module">Comma⇒</a> <a id="3303" href="Categories.Category.Construction.Comma.html#2887" class="Bound">a₁</a> <a id="3306" class="Keyword">renaming</a> <a id="3315" class="Symbol">(</a><a id="3316" href="Categories.Category.Construction.Comma.html#1421" class="Field">g</a> <a id="3318" class="Symbol">to</a> <a id="3321" class="Field">g₁</a><a id="3323" class="Symbol">;</a> <a id="3325" href="Categories.Category.Construction.Comma.html#1451" class="Field">h</a> <a id="3327" class="Symbol">to</a> <a id="3330" class="Field">h₁</a><a id="3332" class="Symbol">;</a> <a id="3334" href="Categories.Category.Construction.Comma.html#1481" class="Field">commute</a> <a id="3342" class="Symbol">to</a> <a id="3345" class="Field">commutes₁</a><a id="3354" class="Symbol">)</a>
<a id="3364" class="Keyword">open</a> <a id="3369" href="Categories.Category.Construction.Comma.html#1094" class="Module">Comma⇒</a> <a id="3376" href="Categories.Category.Construction.Comma.html#2890" class="Bound">a₂</a> <a id="3379" class="Keyword">renaming</a> <a id="3388" class="Symbol">(</a><a id="3389" href="Categories.Category.Construction.Comma.html#1421" class="Field">g</a> <a id="3391" class="Symbol">to</a> <a id="3394" class="Field">g₂</a><a id="3396" class="Symbol">;</a> <a id="3398" href="Categories.Category.Construction.Comma.html#1451" class="Field">h</a> <a id="3400" class="Symbol">to</a> <a id="3403" class="Field">h₂</a><a id="3405" class="Symbol">;</a> <a id="3407" href="Categories.Category.Construction.Comma.html#1481" class="Field">commute</a> <a id="3415" class="Symbol">to</a> <a id="3418" class="Field">commutes₂</a><a id="3427" class="Symbol">)</a>
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<a id="3578" href="Categories.Category.Construction.Comma.html#3578" class="Function Operator">_↓_</a> <a id="3582" class="Symbol">:</a> <a id="3584" class="Symbol">(</a><a id="3585" href="Categories.Category.Construction.Comma.html#3585" class="Bound">S</a> <a id="3587" class="Symbol">:</a> <a id="3589" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="3597" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a> <a id="3599" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a><a id="3600" class="Symbol">)</a> <a id="3602" class="Symbol">(</a><a id="3603" href="Categories.Category.Construction.Comma.html#3603" class="Bound">T</a> <a id="3605" class="Symbol">:</a> <a id="3607" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="3615" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a> <a id="3617" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a><a id="3618" class="Symbol">)</a> <a id="3620" class="Symbol">→</a> <a id="3622" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="3631" class="Symbol">_</a> <a id="3633" class="Symbol">_</a> <a id="3635" class="Symbol">_</a>
<a id="3639" href="Categories.Category.Construction.Comma.html#3639" class="Bound">S</a> <a id="3641" href="Categories.Category.Construction.Comma.html#3578" class="Function Operator">↓</a> <a id="3643" href="Categories.Category.Construction.Comma.html#3643" class="Bound">T</a> <a id="3645" class="Symbol">=</a> <a id="3647" href="Categories.Category.Construction.Comma.html#1532" class="Function">Comma</a> <a id="3653" href="Categories.Category.Construction.Comma.html#3639" class="Bound">S</a> <a id="3655" href="Categories.Category.Construction.Comma.html#3643" class="Bound">T</a>
<a id="3660" href="Categories.Category.Construction.Comma.html#3660" class="Function">Dom</a> <a id="3664" class="Symbol">:</a> <a id="3666" class="Symbol">(</a><a id="3667" href="Categories.Category.Construction.Comma.html#3667" class="Bound">T</a> <a id="3669" class="Symbol">:</a> <a id="3671" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="3679" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a> <a id="3681" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a><a id="3682" class="Symbol">)</a> <a id="3684" class="Symbol">→</a> <a id="3686" class="Symbol">(</a><a id="3687" href="Categories.Category.Construction.Comma.html#3687" class="Bound">S</a> <a id="3689" class="Symbol">:</a> <a id="3691" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="3699" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a> <a id="3701" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a><a id="3702" class="Symbol">)</a> <a id="3704" class="Symbol">→</a> <a id="3706" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="3714" class="Symbol">(</a><a id="3715" href="Categories.Category.Construction.Comma.html#1532" class="Function">Comma</a> <a id="3721" href="Categories.Category.Construction.Comma.html#3667" class="Bound">T</a> <a id="3723" href="Categories.Category.Construction.Comma.html#3687" class="Bound">S</a><a id="3724" class="Symbol">)</a> <a id="3726" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a>
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<a id="3751" class="Symbol">{</a> <a id="3753" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="3756" class="Symbol">=</a> <a id="3758" href="Categories.Category.Construction.Comma.html#1025" class="Field">CommaObj.α</a>
<a id="3773" class="Symbol">;</a> <a id="3775" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="3778" class="Symbol">=</a> <a id="3780" href="Categories.Category.Construction.Comma.html#1421" class="Field">Comma⇒.g</a>
<a id="3793" class="Symbol">;</a> <a id="3795" href="Categories.Functor.Core.html#511" class="Field">identity</a> <a id="3804" class="Symbol">=</a> <a id="3806" href="Relation.Binary.Structures.html#1577" class="Function">refl</a>
<a id="3815" class="Symbol">;</a> <a id="3817" href="Categories.Functor.Core.html#565" class="Field">homomorphism</a> <a id="3830" class="Symbol">=</a> <a id="3832" href="Relation.Binary.Structures.html#1577" class="Function">refl</a>
<a id="3841" class="Symbol">;</a> <a id="3843" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a> <a id="3852" class="Symbol">=</a> <a id="3854" href="Agda.Builtin.Sigma.html#234" class="Field">proj₁</a>
<a id="3864" class="Symbol">}</a>
<a id="3869" class="Keyword">where</a>
<a id="3879" class="Keyword">open</a> <a id="3884" href="Categories.Category.Construction.Comma.html#2266" class="Module">Comma</a> <a id="3890" href="Categories.Category.Construction.Comma.html#3734" class="Bound">T</a> <a id="3892" href="Categories.Category.Construction.Comma.html#3736" class="Bound">S</a>
<a id="3898" class="Keyword">open</a> <a id="3903" href="Categories.Category.Core.html#1530" class="Module">A.Equiv</a>
<a id="3914" href="Categories.Category.Construction.Comma.html#3914" class="Function">Cod</a> <a id="3918" class="Symbol">:</a> <a id="3920" class="Symbol">(</a><a id="3921" href="Categories.Category.Construction.Comma.html#3921" class="Bound">T</a> <a id="3923" class="Symbol">:</a> <a id="3925" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="3933" href="Categories.Category.Construction.Comma.html#664" class="Bound">A</a> <a id="3935" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a><a id="3936" class="Symbol">)</a> <a id="3938" class="Symbol">→</a> <a id="3940" class="Symbol">(</a><a id="3941" href="Categories.Category.Construction.Comma.html#3941" class="Bound">S</a> <a id="3943" class="Symbol">:</a> <a id="3945" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="3953" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a> <a id="3955" href="Categories.Category.Construction.Comma.html#713" class="Bound">C</a><a id="3956" class="Symbol">)</a> <a id="3958" class="Symbol">→</a> <a id="3960" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="3968" class="Symbol">(</a><a id="3969" href="Categories.Category.Construction.Comma.html#1532" class="Function">Comma</a> <a id="3975" href="Categories.Category.Construction.Comma.html#3921" class="Bound">T</a> <a id="3977" href="Categories.Category.Construction.Comma.html#3941" class="Bound">S</a><a id="3978" class="Symbol">)</a> <a id="3980" href="Categories.Category.Construction.Comma.html#689" class="Bound">B</a>
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<a id="4005" class="Symbol">{</a> <a id="4007" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="4010" class="Symbol">=</a> <a id="4012" href="Categories.Category.Construction.Comma.html#1043" class="Field">CommaObj.β</a>
<a id="4027" class="Symbol">;</a> <a id="4029" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="4032" class="Symbol">=</a> <a id="4034" href="Categories.Category.Construction.Comma.html#1451" class="Field">Comma⇒.h</a>
<a id="4047" class="Symbol">;</a> <a id="4049" href="Categories.Functor.Core.html#511" class="Field">identity</a> <a id="4058" class="Symbol">=</a> <a id="4060" href="Relation.Binary.Structures.html#1577" class="Function">refl</a>
<a id="4069" class="Symbol">;</a> <a id="4071" href="Categories.Functor.Core.html#565" class="Field">homomorphism</a> <a id="4084" class="Symbol">=</a> <a id="4086" href="Relation.Binary.Structures.html#1577" class="Function">refl</a>
<a id="4095" class="Symbol">;</a> <a id="4097" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a> <a id="4106" class="Symbol">=</a> <a id="4108" href="Agda.Builtin.Sigma.html#246" class="Field">proj₂</a>
<a id="4118" class="Symbol">}</a>
<a id="4123" class="Keyword">where</a>
<a id="4133" class="Keyword">open</a> <a id="4138" href="Categories.Category.Construction.Comma.html#2266" class="Module">Comma</a> <a id="4144" href="Categories.Category.Construction.Comma.html#3988" class="Bound">T</a> <a id="4146" href="Categories.Category.Construction.Comma.html#3990" class="Bound">S</a>
<a id="4152" class="Keyword">open</a> <a id="4157" href="Categories.Category.Core.html#1530" class="Module">B.Equiv</a>
<a id="4166" class="Keyword">module</a> <a id="4173" href="Categories.Category.Construction.Comma.html#4173" class="Module">_</a> <a id="4175" class="Symbol">{</a><a id="4176" href="Categories.Category.Construction.Comma.html#4176" class="Bound">C</a> <a id="4178" class="Symbol">:</a> <a id="4180" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="4189" href="Categories.Category.Construction.Comma.html#534" class="Generalizable">o₁</a> <a id="4192" href="Categories.Category.Construction.Comma.html#537" class="Generalizable">ℓ₁</a> <a id="4195" href="Categories.Category.Construction.Comma.html#540" class="Generalizable">e₁</a><a id="4197" class="Symbol">}</a> <a id="4199" class="Symbol">{</a><a id="4200" href="Categories.Category.Construction.Comma.html#4200" class="Bound">D</a> <a id="4202" class="Symbol">:</a> <a id="4204" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="4213" href="Categories.Category.Construction.Comma.html#543" class="Generalizable">o₂</a> <a id="4216" href="Categories.Category.Construction.Comma.html#546" class="Generalizable">ℓ₂</a> <a id="4219" href="Categories.Category.Construction.Comma.html#549" class="Generalizable">e₂</a><a id="4221" class="Symbol">}</a> <a id="4223" class="Keyword">where</a>
<a id="4231" class="Keyword">private</a>
<a id="4243" class="Keyword">module</a> <a id="4250" href="Categories.Category.Construction.Comma.html#4250" class="Module">C</a> <a id="4252" class="Symbol">=</a> <a id="4254" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="4263" href="Categories.Category.Construction.Comma.html#4176" class="Bound">C</a>
<a id="4268" class="Keyword">infix</a> <a id="4274" class="Number">4</a> <a id="4276" href="Categories.Category.Construction.Comma.html#4286" class="Function Operator">_↙_</a> <a id="4280" href="Categories.Category.Construction.Comma.html#4365" class="Function Operator">_↘_</a>
<a id="4286" href="Categories.Category.Construction.Comma.html#4286" class="Function Operator">_↙_</a> <a id="4290" class="Symbol">:</a> <a id="4292" class="Symbol">(</a><a id="4293" href="Categories.Category.Construction.Comma.html#4293" class="Bound">X</a> <a id="4295" class="Symbol">:</a> <a id="4297" href="Categories.Category.Core.html#559" class="Function">C.Obj</a><a id="4302" class="Symbol">)</a> <a id="4304" class="Symbol">(</a><a id="4305" href="Categories.Category.Construction.Comma.html#4305" class="Bound">T</a> <a id="4307" class="Symbol">:</a> <a id="4309" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="4317" href="Categories.Category.Construction.Comma.html#4200" class="Bound">D</a> <a id="4319" href="Categories.Category.Construction.Comma.html#4176" class="Bound">C</a><a id="4320" class="Symbol">)</a> <a id="4322" class="Symbol">→</a> <a id="4324" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="4333" class="Symbol">_</a> <a id="4335" class="Symbol">_</a> <a id="4337" class="Symbol">_</a>
<a id="4341" href="Categories.Category.Construction.Comma.html#4341" class="Bound">X</a> <a id="4343" href="Categories.Category.Construction.Comma.html#4286" class="Function Operator">↙</a> <a id="4345" href="Categories.Category.Construction.Comma.html#4345" class="Bound">T</a> <a id="4347" class="Symbol">=</a> <a id="4349" href="Categories.Functor.Construction.Constant.html#719" class="Function">const!</a> <a id="4356" href="Categories.Category.Construction.Comma.html#4341" class="Bound">X</a> <a id="4358" href="Categories.Category.Construction.Comma.html#3578" class="Function Operator">↓</a> <a id="4360" href="Categories.Category.Construction.Comma.html#4345" class="Bound">T</a>
<a id="4365" href="Categories.Category.Construction.Comma.html#4365" class="Function Operator">_↘_</a> <a id="4369" class="Symbol">:</a> <a id="4371" class="Symbol">(</a><a id="4372" href="Categories.Category.Construction.Comma.html#4372" class="Bound">S</a> <a id="4374" class="Symbol">:</a> <a id="4376" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="4384" href="Categories.Category.Construction.Comma.html#4200" class="Bound">D</a> <a id="4386" href="Categories.Category.Construction.Comma.html#4176" class="Bound">C</a><a id="4387" class="Symbol">)</a> <a id="4389" class="Symbol">(</a><a id="4390" href="Categories.Category.Construction.Comma.html#4390" class="Bound">X</a> <a id="4392" class="Symbol">:</a> <a id="4394" href="Categories.Category.Core.html#559" class="Function">C.Obj</a><a id="4399" class="Symbol">)</a> <a id="4401" class="Symbol">→</a> <a id="4403" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="4412" class="Symbol">_</a> <a id="4414" class="Symbol">_</a> <a id="4416" class="Symbol">_</a>
<a id="4420" href="Categories.Category.Construction.Comma.html#4420" class="Bound">S</a> <a id="4422" href="Categories.Category.Construction.Comma.html#4365" class="Function Operator">↘</a> <a id="4424" href="Categories.Category.Construction.Comma.html#4424" class="Bound">X</a> <a id="4426" class="Symbol">=</a> <a id="4428" href="Categories.Category.Construction.Comma.html#4420" class="Bound">S</a> <a id="4430" href="Categories.Category.Construction.Comma.html#3578" class="Function Operator">↓</a> <a id="4432" href="Categories.Functor.Construction.Constant.html#719" class="Function">const!</a> <a id="4439" href="Categories.Category.Construction.Comma.html#4424" class="Bound">X</a>
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