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bsc-leon-vatthauer/agda/bsc-thesis/Categories.Category.Construction.Comma.html
Leon Vatthauer 2bf4655eae
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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.Base.html#1618" class="Function Operator">_×_</a><a id="124" class="Symbol">;</a> <a id="126" href="Data.Product.Base.html#852" class="Function">∃</a><a id="127" class="Symbol">;</a> <a id="129" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">_,_</a><a id="132" class="Symbol">;</a> <a id="134" href="Data.Product.Base.html#636" class="Field">proj₁</a><a id="139" class="Symbol">;</a> <a id="141" href="Data.Product.Base.html#650" class="Field">proj₂</a><a id="146" class="Symbol">;</a> <a id="148" href="Data.Product.Base.html#2747" class="Function">zip</a><a id="151" class="Symbol">;</a> <a id="153" href="Data.Product.Base.html#2173" 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#896" 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#742" 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#388" 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#961" 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#961" 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#388" 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#961" 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#961" 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="1578" href="Categories.Category.Construction.Comma.html#677" class="Bound">o₁</a> <a id="1581" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1583" href="Categories.Category.Construction.Comma.html#702" class="Bound">o₂</a> <a id="1586" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1588" href="Categories.Category.Construction.Comma.html#729" class="Bound">ℓ₃</a><a id="1590" class="Symbol">)</a> <a id="1592" class="Symbol">(</a><a id="1593" href="Categories.Category.Construction.Comma.html#680" class="Bound">ℓ₁</a> <a id="1596" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1598" href="Categories.Category.Construction.Comma.html#705" class="Bound">ℓ₂</a> <a id="1601" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1603" href="Categories.Category.Construction.Comma.html#732" class="Bound">e₃</a><a id="1605" class="Symbol">)</a> <a id="1607" class="Symbol">(</a><a id="1608" href="Categories.Category.Construction.Comma.html#683" class="Bound">e₁</a> <a id="1611" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1613" href="Categories.Category.Construction.Comma.html#708" class="Bound">e₂</a><a id="1615" class="Symbol">)</a>
<a id="1619" href="Categories.Category.Construction.Comma.html#1532" class="Function">Comma</a> <a id="1625" href="Categories.Category.Construction.Comma.html#1625" class="Bound">T</a> <a id="1627" href="Categories.Category.Construction.Comma.html#1627" class="Bound">S</a> <a id="1629" class="Symbol">=</a> <a id="1631" class="Keyword">record</a>
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<a id="1988" class="Symbol">;</a> <a id="1990" href="Categories.Category.Core.html#1145" class="Field">identityʳ</a> <a id="2002" class="Symbol">=</a> <a id="2004" href="Categories.Category.Core.html#1145" class="Function">A.identityʳ</a> <a id="2016" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="2018" href="Categories.Category.Core.html#1145" class="Function">B.identityʳ</a>
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<a id="2191" class="Symbol">;</a> <a id="2193" href="Relation.Binary.Structures.html#1648" class="Field">trans</a> <a id="2199" class="Symbol">=</a> <a id="2201" href="Data.Product.Base.html#2747" class="Function">zip</a> <a id="2205" href="Relation.Binary.Structures.html#1648" class="Function">A.Equiv.trans</a> <a id="2219" href="Relation.Binary.Structures.html#1648" class="Function">B.Equiv.trans</a>
<a id="2239" class="Symbol">}</a>
<a id="2245" class="Symbol">;</a> <a id="2247" href="Categories.Category.Core.html#1438" class="Field">∘-resp-≈</a> <a id="2259" class="Symbol">=</a> <a id="2261" href="Data.Product.Base.html#2747" class="Function">zip</a> <a id="2265" href="Categories.Category.Core.html#1438" class="Function">A.∘-resp-≈</a> <a id="2276" href="Categories.Category.Core.html#1438" class="Function">B.∘-resp-≈</a>
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<a id="2349" class="Keyword">module</a> <a id="2356" href="Categories.Category.Construction.Comma.html#2356" class="Module">S</a> <a id="2358" class="Symbol">=</a> <a id="2360" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="2368" href="Categories.Category.Construction.Comma.html#1627" class="Bound">S</a>
<a id="2377" class="Keyword">open</a> <a id="2382" href="Categories.Category.Construction.Comma.html#2329" class="Module">T</a> <a id="2384" class="Keyword">using</a> <a id="2390" class="Symbol">()</a> <a id="2393" class="Keyword">renaming</a> <a id="2402" class="Symbol">(</a><a id="2403" href="Categories.Functor.Core.html#432" class="Function">F₀</a> <a id="2406" class="Symbol">to</a> <a id="2409" class="Function">T₀</a><a id="2411" class="Symbol">;</a> <a id="2413" href="Categories.Functor.Core.html#455" class="Function">F₁</a> <a id="2416" class="Symbol">to</a> <a id="2419" class="Function">T₁</a><a id="2421" class="Symbol">)</a>
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<a id="2672" href="Categories.Category.Construction.Comma.html#1060" class="Field">f</a> <a id="2686" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="2689" href="Categories.Morphism.Reasoning.Core.html#2899" class="Function">introʳ</a> <a id="2696" href="Categories.Functor.Core.html#511" class="Function">T.identity</a> <a id="2707" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
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<a id="3091" class="Symbol">(</a><a id="3092" href="Categories.Category.Construction.Comma.html#2471" class="Field">S₁</a> <a id="3095" href="Categories.Category.Construction.Comma.html#3364" class="Function">h₁</a> <a id="3098" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="3102" href="Categories.Category.Construction.Comma.html#2471" class="Field">S₁</a> <a id="3105" href="Categories.Category.Construction.Comma.html#3437" class="Field">h₂</a><a id="3107" class="Symbol">)</a> <a id="3109" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="3113" href="Categories.Category.Construction.Comma.html#3503" class="Function">f₁</a> <a id="3116" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">≈⟨</a> <a id="3119" href="Categories.Morphism.Reasoning.Core.html#4290" class="Function">glue</a> <a id="3124" href="Categories.Category.Construction.Comma.html#3379" class="Function">commutes₁</a> <a id="3134" href="Categories.Category.Construction.Comma.html#3452" class="Field">commutes₂</a> <a id="3144" href="Relation.Binary.Reasoning.Syntax.html#7049" class="Function">⟩</a>
<a id="3156" href="Categories.Category.Construction.Comma.html#3591" class="Function">f₃</a> <a id="3159" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="3163" class="Symbol">(</a><a id="3164" href="Categories.Category.Construction.Comma.html#2419" class="Function">T₁</a> <a id="3167" href="Categories.Category.Construction.Comma.html#3355" class="Function">g₁</a> <a id="3170" href="Categories.Category.Core.html#656" class="Field Operator">C.∘</a> <a id="3174" href="Categories.Category.Construction.Comma.html#2419" class="Function">T₁</a> <a id="3177" href="Categories.Category.Construction.Comma.html#3428" class="Field">g₂</a><a id="3179" class="Symbol">)</a> <a id="3181" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">≈˘⟨</a> <a id="3185" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="3193" href="Categories.Functor.Core.html#565" class="Function">T.homomorphism</a> <a id="3208" href="Relation.Binary.Reasoning.Syntax.html#7400" class="Function">⟩</a>
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<a id="4302" class="Keyword">infix</a> <a id="4308" class="Number">4</a> <a id="4310" href="Categories.Category.Construction.Comma.html#4320" class="Function Operator">_↙_</a> <a id="4314" href="Categories.Category.Construction.Comma.html#4416" class="Function Operator">_↘_</a>
<a id="4320" href="Categories.Category.Construction.Comma.html#4320" class="Function Operator">_↙_</a> <a id="4324" class="Symbol">:</a> <a id="4326" class="Symbol">(</a><a id="4327" href="Categories.Category.Construction.Comma.html#4327" class="Bound">X</a> <a id="4329" class="Symbol">:</a> <a id="4331" href="Categories.Category.Core.html#559" class="Function">C.Obj</a><a id="4336" class="Symbol">)</a> <a id="4338" class="Symbol">(</a><a id="4339" href="Categories.Category.Construction.Comma.html#4339" class="Bound">T</a> <a id="4341" class="Symbol">:</a> <a id="4343" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="4351" href="Categories.Category.Construction.Comma.html#4234" class="Bound">D</a> <a id="4353" href="Categories.Category.Construction.Comma.html#4210" class="Bound">C</a><a id="4354" class="Symbol">)</a> <a id="4356" class="Symbol">→</a> <a id="4358" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="4367" class="Symbol">(</a><a id="4368" href="Categories.Category.Construction.Comma.html#4247" class="Bound">o₂</a> <a id="4371" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4373" href="Categories.Category.Construction.Comma.html#4226" class="Bound">ℓ₁</a><a id="4375" class="Symbol">)</a> <a id="4377" class="Symbol">(</a><a id="4378" href="Categories.Category.Construction.Comma.html#4250" class="Bound">ℓ₂</a> <a id="4381" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4383" href="Categories.Category.Construction.Comma.html#4229" class="Bound">e₁</a><a id="4385" class="Symbol">)</a> <a id="4387" href="Categories.Category.Construction.Comma.html#4253" class="Bound">e₂</a>
<a id="4392" href="Categories.Category.Construction.Comma.html#4392" class="Bound">X</a> <a id="4394" href="Categories.Category.Construction.Comma.html#4320" class="Function Operator">↙</a> <a id="4396" href="Categories.Category.Construction.Comma.html#4396" class="Bound">T</a> <a id="4398" class="Symbol">=</a> <a id="4400" href="Categories.Functor.Construction.Constant.html#719" class="Function">const!</a> <a id="4407" href="Categories.Category.Construction.Comma.html#4392" class="Bound">X</a> <a id="4409" href="Categories.Category.Construction.Comma.html#3612" class="Function Operator">↓</a> <a id="4411" href="Categories.Category.Construction.Comma.html#4396" class="Bound">T</a>
<a id="4416" href="Categories.Category.Construction.Comma.html#4416" class="Function Operator">_↘_</a> <a id="4420" class="Symbol">:</a> <a id="4422" class="Symbol">(</a><a id="4423" href="Categories.Category.Construction.Comma.html#4423" class="Bound">S</a> <a id="4425" class="Symbol">:</a> <a id="4427" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="4435" href="Categories.Category.Construction.Comma.html#4234" class="Bound">D</a> <a id="4437" href="Categories.Category.Construction.Comma.html#4210" class="Bound">C</a><a id="4438" class="Symbol">)</a> <a id="4440" class="Symbol">(</a><a id="4441" href="Categories.Category.Construction.Comma.html#4441" class="Bound">X</a> <a id="4443" class="Symbol">:</a> <a id="4445" href="Categories.Category.Core.html#559" class="Function">C.Obj</a><a id="4450" class="Symbol">)</a> <a id="4452" class="Symbol">→</a> <a id="4454" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="4463" class="Symbol">(</a><a id="4464" href="Categories.Category.Construction.Comma.html#4247" class="Bound">o₂</a> <a id="4467" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4469" href="Categories.Category.Construction.Comma.html#4226" class="Bound">ℓ₁</a><a id="4471" class="Symbol">)</a> <a id="4473" class="Symbol">(</a><a id="4474" href="Categories.Category.Construction.Comma.html#4250" class="Bound">ℓ₂</a> <a id="4477" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="4479" href="Categories.Category.Construction.Comma.html#4229" class="Bound">e₁</a><a id="4481" class="Symbol">)</a> <a id="4484" href="Categories.Category.Construction.Comma.html#4253" class="Bound">e₂</a>
<a id="4489" href="Categories.Category.Construction.Comma.html#4489" class="Bound">S</a> <a id="4491" href="Categories.Category.Construction.Comma.html#4416" class="Function Operator">↘</a> <a id="4493" href="Categories.Category.Construction.Comma.html#4493" class="Bound">X</a> <a id="4495" class="Symbol">=</a> <a id="4497" href="Categories.Category.Construction.Comma.html#4489" class="Bound">S</a> <a id="4499" href="Categories.Category.Construction.Comma.html#3612" class="Function Operator">↓</a> <a id="4501" href="Categories.Functor.Construction.Constant.html#719" class="Function">const!</a> <a id="4508" href="Categories.Category.Construction.Comma.html#4493" class="Bound">X</a>
</pre></body></html>
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