leonv/bsc-leon-vatthauer
1
0
Fork 0
mirror of https://git8.cs.fau.de/theses/bsc-leon-vatthauer.git synced 2024-05-31 07:28:34 +02:00
Code Issues Projects Releases Packages Wiki Activity
bsc-leon-vatthauer/public/Categories.Diagram.Cowedge.html

59 lines
No EOL
18 KiB
HTML
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

<!DOCTYPE HTML>
<html><head><meta charset="utf-8"><title>Categories.Diagram.Cowedge</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.Core.html" class="Module">Categories.Category.Core</a> <a id="74" class="Keyword">using</a> <a id="80" class="Symbol">(</a><a id="81" href="Categories.Category.Core.html#442" class="Record">Category</a><a id="89" class="Symbol">)</a>
<a id="91" class="Keyword">open</a> <a id="96" class="Keyword">import</a> <a id="103" href="Categories.Functor.Bifunctor.html" class="Module">Categories.Functor.Bifunctor</a> <a id="132" class="Keyword">using</a> <a id="138" class="Symbol">(</a><a id="139" href="Categories.Functor.Bifunctor.html#441" class="Function">Bifunctor</a><a id="148" class="Symbol">)</a>
<a id="151" class="Keyword">module</a> <a id="158" href="Categories.Diagram.Cowedge.html" class="Module">Categories.Diagram.Cowedge</a> <a id="185" class="Symbol">{</a><a id="186" href="Categories.Diagram.Cowedge.html#186" class="Bound">o</a> <a id="188" href="Categories.Diagram.Cowedge.html#188" class="Bound">ℓ</a> <a id="190" href="Categories.Diagram.Cowedge.html#190" class="Bound">e</a> <a id="192" href="Categories.Diagram.Cowedge.html#192" class="Bound">o′</a> <a id="195" href="Categories.Diagram.Cowedge.html#195" class="Bound">ℓ′</a> <a id="198" href="Categories.Diagram.Cowedge.html#198" class="Bound">e′</a><a id="200" class="Symbol">}</a> <a id="202" class="Symbol">{</a><a id="203" href="Categories.Diagram.Cowedge.html#203" class="Bound">C</a> <a id="205" class="Symbol">:</a> <a id="207" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="216" href="Categories.Diagram.Cowedge.html#186" class="Bound">o</a> <a id="218" href="Categories.Diagram.Cowedge.html#188" class="Bound">ℓ</a> <a id="220" href="Categories.Diagram.Cowedge.html#190" class="Bound">e</a><a id="221" class="Symbol">}</a> <a id="223" class="Symbol">{</a><a id="224" href="Categories.Diagram.Cowedge.html#224" class="Bound">D</a> <a id="226" class="Symbol">:</a> <a id="228" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="237" href="Categories.Diagram.Cowedge.html#192" class="Bound">o′</a> <a id="240" href="Categories.Diagram.Cowedge.html#195" class="Bound">ℓ′</a> <a id="243" href="Categories.Diagram.Cowedge.html#198" class="Bound">e′</a><a id="245" class="Symbol">}</a>
<a id="249" class="Symbol">(</a><a id="250" href="Categories.Diagram.Cowedge.html#250" class="Bound">F</a> <a id="252" class="Symbol">:</a> <a id="254" href="Categories.Functor.Bifunctor.html#441" class="Function">Bifunctor</a> <a id="264" class="Symbol">(</a><a id="265" href="Categories.Category.Core.html#3132" class="Function">Category.op</a> <a id="277" href="Categories.Diagram.Cowedge.html#203" class="Bound">C</a><a id="278" class="Symbol">)</a> <a id="280" href="Categories.Diagram.Cowedge.html#203" class="Bound">C</a> <a id="282" href="Categories.Diagram.Cowedge.html#224" class="Bound">D</a><a id="283" class="Symbol">)</a> <a id="285" class="Keyword">where</a>
<a id="292" class="Keyword">private</a>
<a id="302" class="Keyword">module</a> <a id="C"></a><a id="309" href="Categories.Diagram.Cowedge.html#309" class="Module">C</a> <a id="311" class="Symbol">=</a> <a id="313" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="322" href="Categories.Diagram.Cowedge.html#203" class="Bound">C</a>
<a id="326" class="Keyword">module</a> <a id="D"></a><a id="333" href="Categories.Diagram.Cowedge.html#333" class="Module">D</a> <a id="335" class="Symbol">=</a> <a id="337" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="346" href="Categories.Diagram.Cowedge.html#224" class="Bound">D</a>
<a id="350" class="Keyword">open</a> <a id="355" href="Categories.Diagram.Cowedge.html#333" class="Module">D</a>
<a id="359" class="Keyword">open</a> <a id="364" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
<a id="379" class="Keyword">open</a> <a id="384" href="Categories.Category.Core.html#1530" class="Module">Equiv</a>
<a id="392" class="Keyword">variable</a>
<a id="405" href="Categories.Diagram.Cowedge.html#405" class="Generalizable">A</a> <a id="407" class="Symbol">:</a> <a id="409" href="Categories.Category.Core.html#559" class="Function">Obj</a>
<a id="414" class="Keyword">open</a> <a id="419" class="Keyword">import</a> <a id="426" href="Level.html" class="Module">Level</a>
<a id="433" class="Keyword">open</a> <a id="438" class="Keyword">import</a> <a id="445" href="Categories.Functor.html" class="Module">Categories.Functor</a>
<a id="464" class="Keyword">open</a> <a id="469" class="Keyword">import</a> <a id="476" href="Categories.Functor.Construction.Constant.html" class="Module">Categories.Functor.Construction.Constant</a>
<a id="517" class="Keyword">open</a> <a id="522" class="Keyword">import</a> <a id="529" href="Categories.NaturalTransformation.Dinatural.html" class="Module">Categories.NaturalTransformation.Dinatural</a>
<a id="573" class="Keyword">open</a> <a id="578" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="586" href="Categories.Diagram.Cowedge.html#250" class="Bound">F</a>
<a id="589" class="Keyword">record</a> <a id="Cowedge"></a><a id="596" href="Categories.Diagram.Cowedge.html#596" class="Record">Cowedge</a> <a id="604" class="Symbol">:</a> <a id="606" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="610" class="Symbol">(</a><a id="611" href="Level.html#602" class="Function">levelOfTerm</a> <a id="623" href="Categories.Diagram.Cowedge.html#250" class="Bound">F</a><a id="624" class="Symbol">)</a> <a id="626" class="Keyword">where</a>
<a id="634" class="Keyword">field</a>
<a id="Cowedge.E"></a><a id="644" href="Categories.Diagram.Cowedge.html#644" class="Field">E</a> <a id="654" class="Symbol">:</a> <a id="656" href="Categories.Category.Core.html#559" class="Function">Obj</a>
<a id="Cowedge.dinatural"></a><a id="664" href="Categories.Diagram.Cowedge.html#664" class="Field">dinatural</a> <a id="674" class="Symbol">:</a> <a id="676" href="Categories.NaturalTransformation.Dinatural.html#578" class="Record">DinaturalTransformation</a> <a id="700" href="Categories.Diagram.Cowedge.html#250" class="Bound">F</a> <a id="702" class="Symbol">(</a><a id="703" href="Categories.Functor.Construction.Constant.html#461" class="Function">const</a> <a id="709" href="Categories.Diagram.Cowedge.html#644" class="Field">E</a><a id="710" class="Symbol">)</a>
<a id="715" class="Keyword">module</a> <a id="Cowedge.dinatural"></a><a id="722" href="Categories.Diagram.Cowedge.html#722" class="Module">dinatural</a> <a id="732" class="Symbol">=</a> <a id="734" href="Categories.NaturalTransformation.Dinatural.html#578" class="Module">DinaturalTransformation</a> <a id="758" href="Categories.Diagram.Cowedge.html#664" class="Field">dinatural</a>
<a id="Cowedge-∘"></a><a id="769" href="Categories.Diagram.Cowedge.html#769" class="Function">Cowedge-∘</a> <a id="779" class="Symbol">:</a> <a id="781" class="Symbol">(</a><a id="782" href="Categories.Diagram.Cowedge.html#782" class="Bound">W</a> <a id="784" class="Symbol">:</a> <a id="786" href="Categories.Diagram.Cowedge.html#596" class="Record">Cowedge</a><a id="793" class="Symbol">)</a> <a id="795" class="Symbol">→</a> <a id="797" href="Categories.Diagram.Cowedge.html#644" class="Field">Cowedge.E</a> <a id="807" href="Categories.Diagram.Cowedge.html#782" class="Bound">W</a> <a id="809" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="811" href="Categories.Diagram.Cowedge.html#405" class="Generalizable">A</a> <a id="813" class="Symbol">→</a> <a id="815" href="Categories.Diagram.Cowedge.html#596" class="Record">Cowedge</a>
<a id="823" href="Categories.Diagram.Cowedge.html#769" class="Function">Cowedge-∘</a> <a id="833" class="Symbol">{</a><a id="834" class="Argument">A</a> <a id="836" class="Symbol">=</a> <a id="838" href="Categories.Diagram.Cowedge.html#838" class="Bound">A</a><a id="839" class="Symbol">}</a> <a id="841" href="Categories.Diagram.Cowedge.html#841" class="Bound">W</a> <a id="843" href="Categories.Diagram.Cowedge.html#843" class="Bound">f</a> <a id="845" class="Symbol">=</a> <a id="847" class="Keyword">record</a>
<a id="856" class="Symbol">{</a> <a id="858" href="Categories.Diagram.Cowedge.html#644" class="Field">E</a> <a id="868" class="Symbol">=</a> <a id="870" href="Categories.Diagram.Cowedge.html#838" class="Bound">A</a>
<a id="874" class="Symbol">;</a> <a id="876" href="Categories.Diagram.Cowedge.html#664" class="Field">dinatural</a> <a id="886" class="Symbol">=</a> <a id="888" href="Categories.NaturalTransformation.Dinatural.html#7753" class="Function">extranaturalˡ</a> <a id="902" class="Symbol">(λ</a> <a id="905" href="Categories.Diagram.Cowedge.html#905" class="Bound">X</a> <a id="907" class="Symbol">→</a> <a id="909" href="Categories.Diagram.Cowedge.html#843" class="Bound">f</a> <a id="911" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="913" href="Categories.NaturalTransformation.Dinatural.html#851" class="Function">dinatural.α</a> <a id="925" href="Categories.Diagram.Cowedge.html#905" class="Bound">X</a><a id="926" class="Symbol">)</a>
<a id="958" class="Symbol">(</a><a id="959" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="965" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="967" href="Categories.Category.Core.html#1706" class="Function">∘-resp-≈ʳ</a> <a id="977" class="Symbol">(</a><a id="978" href="Categories.NaturalTransformation.Dinatural.html#8047" class="Function">extranatural-commˡ</a> <a id="997" href="Categories.Diagram.Cowedge.html#664" class="Function">dinatural</a><a id="1006" class="Symbol">)</a> <a id="1008" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="1010" href="Categories.Category.Core.html#1004" class="Function">sym-assoc</a><a id="1019" class="Symbol">)</a>
<a id="1023" class="Symbol">}</a>
<a id="1027" class="Keyword">where</a> <a id="1033" class="Keyword">open</a> <a id="1038" href="Categories.Diagram.Cowedge.html#596" class="Module">Cowedge</a> <a id="1046" href="Categories.Diagram.Cowedge.html#841" class="Bound">W</a>
<a id="1049" class="Keyword">record</a> <a id="Cowedge-Morphism"></a><a id="1056" href="Categories.Diagram.Cowedge.html#1056" class="Record">Cowedge-Morphism</a> <a id="1073" class="Symbol">(</a><a id="1074" href="Categories.Diagram.Cowedge.html#1074" class="Bound">W₁</a> <a id="1077" href="Categories.Diagram.Cowedge.html#1077" class="Bound">W₂</a> <a id="1080" class="Symbol">:</a> <a id="1082" href="Categories.Diagram.Cowedge.html#596" class="Record">Cowedge</a><a id="1089" class="Symbol">)</a> <a id="1091" class="Symbol">:</a> <a id="1093" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1097" class="Symbol">(</a><a id="1098" href="Level.html#602" class="Function">levelOfTerm</a> <a id="1110" href="Categories.Diagram.Cowedge.html#250" class="Bound">F</a><a id="1111" class="Symbol">)</a> <a id="1113" class="Keyword">where</a>
<a id="1121" class="Keyword">private</a>
<a id="1133" class="Keyword">module</a> <a id="Cowedge-Morphism.W₁"></a><a id="1140" href="Categories.Diagram.Cowedge.html#1140" class="Module">W₁</a> <a id="1143" class="Symbol">=</a> <a id="1145" href="Categories.Diagram.Cowedge.html#596" class="Module">Cowedge</a> <a id="1153" href="Categories.Diagram.Cowedge.html#1074" class="Bound">W₁</a>
<a id="1160" class="Keyword">module</a> <a id="Cowedge-Morphism.W₂"></a><a id="1167" href="Categories.Diagram.Cowedge.html#1167" class="Module">W₂</a> <a id="1170" class="Symbol">=</a> <a id="1172" href="Categories.Diagram.Cowedge.html#596" class="Module">Cowedge</a> <a id="1180" href="Categories.Diagram.Cowedge.html#1077" class="Bound">W₂</a>
<a id="1187" class="Keyword">open</a> <a id="1192" href="Categories.NaturalTransformation.Dinatural.html#578" class="Module">DinaturalTransformation</a>
<a id="1218" class="Keyword">field</a>
<a id="Cowedge-Morphism.u"></a><a id="1228" href="Categories.Diagram.Cowedge.html#1228" class="Field">u</a> <a id="1230" class="Symbol">:</a> <a id="1232" href="Categories.Diagram.Cowedge.html#644" class="Function">W₁.E</a> <a id="1237" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="1239" href="Categories.Diagram.Cowedge.html#644" class="Function">W₂.E</a>
<a id="Cowedge-Morphism.commute"></a><a id="1248" href="Categories.Diagram.Cowedge.html#1248" class="Field">commute</a> <a id="1256" class="Symbol">:</a> <a id="1258" class="Symbol">∀</a> <a id="1260" class="Symbol">{</a><a id="1261" href="Categories.Diagram.Cowedge.html#1261" class="Bound">C</a><a id="1262" class="Symbol">}</a> <a id="1264" class="Symbol">→</a> <a id="1266" href="Categories.Diagram.Cowedge.html#1228" class="Field">u</a> <a id="1268" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1270" href="Categories.NaturalTransformation.Dinatural.html#851" class="Function">W₁.dinatural.α</a> <a id="1285" href="Categories.Diagram.Cowedge.html#1261" class="Bound">C</a> <a id="1287" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="1289" href="Categories.NaturalTransformation.Dinatural.html#851" class="Function">W₂.dinatural.α</a> <a id="1304" href="Categories.Diagram.Cowedge.html#1261" class="Bound">C</a>
<a id="Cowedge-id"></a><a id="1307" href="Categories.Diagram.Cowedge.html#1307" class="Function">Cowedge-id</a> <a id="1318" class="Symbol">:</a> <a id="1320" class="Symbol">∀</a> <a id="1322" class="Symbol">{</a><a id="1323" href="Categories.Diagram.Cowedge.html#1323" class="Bound">W</a><a id="1324" class="Symbol">}</a> <a id="1326" class="Symbol">→</a> <a id="1328" href="Categories.Diagram.Cowedge.html#1056" class="Record">Cowedge-Morphism</a> <a id="1345" href="Categories.Diagram.Cowedge.html#1323" class="Bound">W</a> <a id="1347" href="Categories.Diagram.Cowedge.html#1323" class="Bound">W</a>
<a id="1349" href="Categories.Diagram.Cowedge.html#1307" class="Function">Cowedge-id</a> <a id="1360" class="Symbol">{</a><a id="1361" href="Categories.Diagram.Cowedge.html#1361" class="Bound">W</a><a id="1362" class="Symbol">}</a> <a id="1364" class="Symbol">=</a> <a id="1366" class="Keyword">record</a> <a id="1373" class="Symbol">{</a> <a id="1375" href="Categories.Diagram.Cowedge.html#1228" class="Field">u</a> <a id="1377" class="Symbol">=</a> <a id="1379" href="Categories.Category.Core.html#630" class="Function">D.id</a> <a id="1384" class="Symbol">;</a> <a id="1386" href="Categories.Diagram.Cowedge.html#1248" class="Field">commute</a> <a id="1394" class="Symbol">=</a> <a id="1396" href="Categories.Category.Core.html#1096" class="Function">D.identityˡ</a> <a id="1408" class="Symbol">}</a>
<a id="Cowedge-Morphism-∘"></a><a id="1411" href="Categories.Diagram.Cowedge.html#1411" class="Function">Cowedge-Morphism-∘</a> <a id="1430" class="Symbol">:</a> <a id="1432" class="Symbol">{</a><a id="1433" href="Categories.Diagram.Cowedge.html#1433" class="Bound">A</a> <a id="1435" href="Categories.Diagram.Cowedge.html#1435" class="Bound">B</a> <a id="1437" href="Categories.Diagram.Cowedge.html#1437" class="Bound">C</a> <a id="1439" class="Symbol">:</a> <a id="1441" href="Categories.Diagram.Cowedge.html#596" class="Record">Cowedge</a><a id="1448" class="Symbol">}</a> <a id="1450" class="Symbol">→</a> <a id="1452" href="Categories.Diagram.Cowedge.html#1056" class="Record">Cowedge-Morphism</a> <a id="1469" href="Categories.Diagram.Cowedge.html#1435" class="Bound">B</a> <a id="1471" href="Categories.Diagram.Cowedge.html#1437" class="Bound">C</a> <a id="1473" class="Symbol">→</a> <a id="1475" href="Categories.Diagram.Cowedge.html#1056" class="Record">Cowedge-Morphism</a> <a id="1492" href="Categories.Diagram.Cowedge.html#1433" class="Bound">A</a> <a id="1494" href="Categories.Diagram.Cowedge.html#1435" class="Bound">B</a> <a id="1496" class="Symbol">→</a> <a id="1498" href="Categories.Diagram.Cowedge.html#1056" class="Record">Cowedge-Morphism</a> <a id="1515" href="Categories.Diagram.Cowedge.html#1433" class="Bound">A</a> <a id="1517" href="Categories.Diagram.Cowedge.html#1437" class="Bound">C</a>
<a id="1519" href="Categories.Diagram.Cowedge.html#1411" class="Function">Cowedge-Morphism-∘</a> <a id="1538" href="Categories.Diagram.Cowedge.html#1538" class="Bound">M</a> <a id="1540" href="Categories.Diagram.Cowedge.html#1540" class="Bound">N</a> <a id="1542" class="Symbol">=</a> <a id="1544" class="Keyword">record</a> <a id="1551" class="Symbol">{</a> <a id="1553" href="Categories.Diagram.Cowedge.html#1228" class="Field">u</a> <a id="1555" class="Symbol">=</a> <a id="1557" href="Categories.Diagram.Cowedge.html#1228" class="Field">u</a> <a id="1559" href="Categories.Diagram.Cowedge.html#1538" class="Bound">M</a> <a id="1561" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1563" href="Categories.Diagram.Cowedge.html#1228" class="Field">u</a> <a id="1565" href="Categories.Diagram.Cowedge.html#1540" class="Bound">N</a> <a id="1567" class="Symbol">;</a> <a id="1569" href="Categories.Diagram.Cowedge.html#1248" class="Field">commute</a> <a id="1577" class="Symbol">=</a> <a id="1579" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="1585" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="1587" class="Symbol">(</a><a id="1588" href="Categories.Category.Core.html#1706" class="Function">∘-resp-≈ʳ</a> <a id="1598" class="Symbol">(</a><a id="1599" href="Categories.Diagram.Cowedge.html#1248" class="Field">commute</a> <a id="1607" href="Categories.Diagram.Cowedge.html#1540" class="Bound">N</a><a id="1608" class="Symbol">)</a> <a id="1610" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="1612" href="Categories.Diagram.Cowedge.html#1248" class="Field">commute</a> <a id="1620" href="Categories.Diagram.Cowedge.html#1538" class="Bound">M</a><a id="1621" class="Symbol">)</a> <a id="1623" class="Symbol">}</a>
<a id="1627" class="Keyword">where</a>
<a id="1635" class="Keyword">open</a> <a id="1640" href="Categories.Diagram.Cowedge.html#1056" class="Module">Cowedge-Morphism</a>
<a id="1659" class="Keyword">open</a> <a id="1664" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
</pre></body></html>
Reference in a new issue View git blame Copy permalink