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.Cone.Properties.html

103 lines
No EOL
32 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.Cone.Properties</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">module</a> <a id="44" href="Categories.Diagram.Cone.Properties.html" class="Module">Categories.Diagram.Cone.Properties</a> <a id="79" class="Keyword">where</a>
<a id="86" class="Keyword">open</a> <a id="91" class="Keyword">import</a> <a id="98" href="Level.html" class="Module">Level</a>
<a id="105" class="Keyword">open</a> <a id="110" class="Keyword">import</a> <a id="117" href="Categories.Category.html" class="Module">Categories.Category</a>
<a id="137" class="Keyword">open</a> <a id="142" class="Keyword">import</a> <a id="149" href="Categories.Functor.html" class="Module">Categories.Functor</a>
<a id="168" class="Keyword">open</a> <a id="173" class="Keyword">import</a> <a id="180" href="Categories.Functor.Properties.html" class="Module">Categories.Functor.Properties</a>
<a id="210" class="Keyword">open</a> <a id="215" class="Keyword">import</a> <a id="222" href="Categories.NaturalTransformation.html" class="Module">Categories.NaturalTransformation</a>
<a id="255" class="Keyword">import</a> <a id="262" href="Categories.Diagram.Cone.html" class="Module">Categories.Diagram.Cone</a> <a id="286" class="Symbol">as</a> <a id="289" class="Module">Con</a>
<a id="293" class="Keyword">import</a> <a id="300" href="Categories.Morphism.Reasoning.html" class="Module">Categories.Morphism.Reasoning</a> <a id="330" class="Symbol">as</a> <a id="333" class="Module">MR</a>
<a id="337" class="Keyword">private</a>
<a id="347" class="Keyword">variable</a>
<a id="360" href="Categories.Diagram.Cone.Properties.html#360" class="Generalizable">o</a> <a id="362" href="Categories.Diagram.Cone.Properties.html#362" class="Generalizable">ℓ</a> <a id="364" href="Categories.Diagram.Cone.Properties.html#364" class="Generalizable">e</a> <a id="366" class="Symbol">:</a> <a id="368" href="Agda.Primitive.html#591" class="Postulate">Level</a>
<a id="378" href="Categories.Diagram.Cone.Properties.html#378" class="Generalizable">C</a> <a id="380" href="Categories.Diagram.Cone.Properties.html#380" class="Generalizable">D</a> <a id="382" href="Categories.Diagram.Cone.Properties.html#382" class="Generalizable">J</a> <a id="384" href="Categories.Diagram.Cone.Properties.html#384" class="Generalizable">J′</a> <a id="387" class="Symbol">:</a> <a id="389" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="398" href="Categories.Diagram.Cone.Properties.html#360" class="Generalizable">o</a> <a id="400" href="Categories.Diagram.Cone.Properties.html#362" class="Generalizable">ℓ</a> <a id="402" href="Categories.Diagram.Cone.Properties.html#364" class="Generalizable">e</a>
<a id="405" class="Keyword">module</a> <a id="412" href="Categories.Diagram.Cone.Properties.html#412" class="Module">_</a> <a id="414" class="Symbol">{</a><a id="415" href="Categories.Diagram.Cone.Properties.html#415" class="Bound">F</a> <a id="417" class="Symbol">:</a> <a id="419" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="427" href="Categories.Diagram.Cone.Properties.html#382" class="Generalizable">J</a> <a id="429" href="Categories.Diagram.Cone.Properties.html#378" class="Generalizable">C</a><a id="430" class="Symbol">}</a> <a id="432" class="Symbol">(</a><a id="433" href="Categories.Diagram.Cone.Properties.html#433" class="Bound">G</a> <a id="435" class="Symbol">:</a> <a id="437" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="445" href="Categories.Diagram.Cone.Properties.html#378" class="Generalizable">C</a> <a id="447" href="Categories.Diagram.Cone.Properties.html#380" class="Generalizable">D</a><a id="448" class="Symbol">)</a> <a id="450" class="Keyword">where</a>
<a id="458" class="Keyword">private</a>
<a id="470" class="Keyword">module</a> <a id="477" href="Categories.Diagram.Cone.Properties.html#477" class="Module">C</a> <a id="479" class="Symbol">=</a> <a id="481" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="490" href="Categories.Diagram.Cone.Properties.html#429" class="Bound">C</a>
<a id="496" class="Keyword">module</a> <a id="503" href="Categories.Diagram.Cone.Properties.html#503" class="Module">D</a> <a id="505" class="Symbol">=</a> <a id="507" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="516" href="Categories.Diagram.Cone.Properties.html#447" class="Bound">D</a>
<a id="522" class="Keyword">module</a> <a id="529" href="Categories.Diagram.Cone.Properties.html#529" class="Module">F</a> <a id="531" class="Symbol">=</a> <a id="533" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="541" href="Categories.Diagram.Cone.Properties.html#415" class="Bound">F</a>
<a id="547" class="Keyword">module</a> <a id="554" href="Categories.Diagram.Cone.Properties.html#554" class="Module">G</a> <a id="556" class="Symbol">=</a> <a id="558" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="566" href="Categories.Diagram.Cone.Properties.html#433" class="Bound">G</a>
<a id="572" class="Keyword">module</a> <a id="579" href="Categories.Diagram.Cone.Properties.html#579" class="Module">CF</a> <a id="582" class="Symbol">=</a> <a id="584" href="Categories.Diagram.Cone.html" class="Module">Con</a> <a id="588" href="Categories.Diagram.Cone.Properties.html#415" class="Bound">F</a>
<a id="594" href="Categories.Diagram.Cone.Properties.html#594" class="Function">GF</a> <a id="597" class="Symbol">=</a> <a id="599" href="Categories.Diagram.Cone.Properties.html#433" class="Bound">G</a> <a id="601" href="Categories.Functor.html#747" class="Function Operator">∘F</a> <a id="604" href="Categories.Diagram.Cone.Properties.html#415" class="Bound">F</a>
<a id="610" class="Keyword">module</a> <a id="617" href="Categories.Diagram.Cone.Properties.html#617" class="Module">CGF</a> <a id="621" class="Symbol">=</a> <a id="623" href="Categories.Diagram.Cone.html" class="Module">Con</a> <a id="627" href="Categories.Diagram.Cone.Properties.html#594" class="Function">GF</a>
<a id="633" href="Categories.Diagram.Cone.Properties.html#633" class="Function">F-map-Coneˡ</a> <a id="645" class="Symbol">:</a> <a id="647" href="Categories.Diagram.Cone.html#526" class="Record">CF.Cone</a> <a id="655" class="Symbol">→</a> <a id="657" href="Categories.Diagram.Cone.html#526" class="Record">CGF.Cone</a>
<a id="668" href="Categories.Diagram.Cone.Properties.html#633" class="Function">F-map-Coneˡ</a> <a id="680" href="Categories.Diagram.Cone.Properties.html#680" class="Bound">K</a> <a id="682" class="Symbol">=</a> <a id="684" class="Keyword">record</a>
<a id="695" class="Symbol">{</a> <a id="697" href="Categories.Diagram.Cone.html#592" class="Field">apex</a> <a id="702" class="Symbol">=</a> <a id="704" class="Keyword">record</a>
<a id="717" class="Symbol">{</a> <a id="719" href="Categories.Diagram.Cone.html#415" class="Field">ψ</a> <a id="727" class="Symbol">=</a> <a id="729" class="Symbol">λ</a> <a id="731" href="Categories.Diagram.Cone.Properties.html#731" class="Bound">X</a> <a id="733" class="Symbol">→</a> <a id="735" href="Categories.Functor.Core.html#455" class="Field">G.F₁</a> <a id="740" class="Symbol">(</a><a id="741" href="Categories.Diagram.Cone.html#415" class="Function">ψ</a> <a id="743" href="Categories.Diagram.Cone.Properties.html#731" class="Bound">X</a><a id="744" class="Symbol">)</a>
<a id="752" class="Symbol">;</a> <a id="754" href="Categories.Diagram.Cone.html#463" class="Field">commute</a> <a id="762" class="Symbol">=</a> <a id="764" class="Symbol">λ</a> <a id="766" href="Categories.Diagram.Cone.Properties.html#766" class="Bound">f</a> <a id="768" class="Symbol">→</a> <a id="770" href="Categories.Functor.Properties.html#2426" class="Function Operator">[</a> <a id="772" href="Categories.Diagram.Cone.Properties.html#433" class="Bound">G</a> <a id="774" href="Categories.Functor.Properties.html#2426" class="Function Operator">]-resp-∘</a> <a id="783" class="Symbol">(</a><a id="784" href="Categories.Diagram.Cone.html#463" class="Function">commute</a> <a id="792" href="Categories.Diagram.Cone.Properties.html#766" class="Bound">f</a><a id="793" class="Symbol">)</a>
<a id="801" class="Symbol">}</a>
<a id="807" class="Symbol">}</a>
<a id="813" class="Keyword">where</a> <a id="819" class="Keyword">open</a> <a id="824" href="Categories.Diagram.Cone.html#526" class="Module">CF.Cone</a> <a id="832" href="Categories.Diagram.Cone.Properties.html#680" class="Bound">K</a>
<a id="837" href="Categories.Diagram.Cone.Properties.html#837" class="Function">F-map-Cone⇒ˡ</a> <a id="850" class="Symbol">:</a> <a id="852" class="Symbol">∀</a> <a id="854" class="Symbol">{</a><a id="855" href="Categories.Diagram.Cone.Properties.html#855" class="Bound">K</a> <a id="857" href="Categories.Diagram.Cone.Properties.html#857" class="Bound">K′</a><a id="859" class="Symbol">}</a> <a id="861" class="Symbol">(</a><a id="862" href="Categories.Diagram.Cone.Properties.html#862" class="Bound">f</a> <a id="864" class="Symbol">:</a> <a id="866" href="Categories.Diagram.Cone.html#660" class="Record">CF.Cone⇒</a> <a id="875" href="Categories.Diagram.Cone.Properties.html#855" class="Bound">K</a> <a id="877" href="Categories.Diagram.Cone.Properties.html#857" class="Bound">K′</a><a id="879" class="Symbol">)</a> <a id="881" class="Symbol">→</a> <a id="883" href="Categories.Diagram.Cone.html#660" class="Record">CGF.Cone⇒</a> <a id="893" class="Symbol">(</a><a id="894" href="Categories.Diagram.Cone.Properties.html#633" class="Function">F-map-Coneˡ</a> <a id="906" href="Categories.Diagram.Cone.Properties.html#855" class="Bound">K</a><a id="907" class="Symbol">)</a> <a id="909" class="Symbol">(</a><a id="910" href="Categories.Diagram.Cone.Properties.html#633" class="Function">F-map-Coneˡ</a> <a id="922" href="Categories.Diagram.Cone.Properties.html#857" class="Bound">K′</a><a id="924" class="Symbol">)</a>
<a id="928" href="Categories.Diagram.Cone.Properties.html#837" class="Function">F-map-Cone⇒ˡ</a> <a id="941" href="Categories.Diagram.Cone.Properties.html#941" class="Bound">f</a> <a id="943" class="Symbol">=</a> <a id="945" class="Keyword">record</a>
<a id="956" class="Symbol">{</a> <a id="958" href="Categories.Diagram.Cone.html#717" class="Field">arr</a> <a id="966" class="Symbol">=</a> <a id="968" href="Categories.Functor.Core.html#455" class="Field">G.F₁</a> <a id="973" href="Categories.Diagram.Cone.html#717" class="Field">arr</a>
<a id="981" class="Symbol">;</a> <a id="983" href="Categories.Diagram.Cone.html#742" class="Field">commute</a> <a id="991" class="Symbol">=</a> <a id="993" href="Categories.Functor.Properties.html#2426" class="Function Operator">[</a> <a id="995" href="Categories.Diagram.Cone.Properties.html#433" class="Bound">G</a> <a id="997" href="Categories.Functor.Properties.html#2426" class="Function Operator">]-resp-∘</a> <a id="1006" href="Categories.Diagram.Cone.html#742" class="Field">commute</a>
<a id="1018" class="Symbol">}</a>
<a id="1024" class="Keyword">where</a> <a id="1030" class="Keyword">open</a> <a id="1035" href="Categories.Diagram.Cone.html#660" class="Module">CF.Cone⇒</a> <a id="1044" href="Categories.Diagram.Cone.Properties.html#941" class="Bound">f</a>
<a id="1047" class="Keyword">module</a> <a id="1054" href="Categories.Diagram.Cone.Properties.html#1054" class="Module">_</a> <a id="1056" class="Symbol">{</a><a id="1057" href="Categories.Diagram.Cone.Properties.html#1057" class="Bound">F</a> <a id="1059" class="Symbol">:</a> <a id="1061" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1069" href="Categories.Diagram.Cone.Properties.html#382" class="Generalizable">J</a> <a id="1071" href="Categories.Diagram.Cone.Properties.html#378" class="Generalizable">C</a><a id="1072" class="Symbol">}</a> <a id="1074" class="Symbol">(</a><a id="1075" href="Categories.Diagram.Cone.Properties.html#1075" class="Bound">G</a> <a id="1077" class="Symbol">:</a> <a id="1079" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1087" href="Categories.Diagram.Cone.Properties.html#384" class="Generalizable">J′</a> <a id="1090" href="Categories.Diagram.Cone.Properties.html#382" class="Generalizable">J</a><a id="1091" class="Symbol">)</a> <a id="1093" class="Keyword">where</a>
<a id="1101" class="Keyword">private</a>
<a id="1113" class="Keyword">module</a> <a id="1120" href="Categories.Diagram.Cone.Properties.html#1120" class="Module">C</a> <a id="1124" class="Symbol">=</a> <a id="1126" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="1135" href="Categories.Diagram.Cone.Properties.html#1071" class="Bound">C</a>
<a id="1141" class="Keyword">module</a> <a id="1148" href="Categories.Diagram.Cone.Properties.html#1148" class="Module">J′</a> <a id="1152" class="Symbol">=</a> <a id="1154" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="1163" href="Categories.Diagram.Cone.Properties.html#1087" class="Bound">J′</a>
<a id="1170" class="Keyword">module</a> <a id="1177" href="Categories.Diagram.Cone.Properties.html#1177" class="Module">F</a> <a id="1181" class="Symbol">=</a> <a id="1183" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="1191" href="Categories.Diagram.Cone.Properties.html#1057" class="Bound">F</a>
<a id="1197" class="Keyword">module</a> <a id="1204" href="Categories.Diagram.Cone.Properties.html#1204" class="Module">G</a> <a id="1208" class="Symbol">=</a> <a id="1210" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="1218" href="Categories.Diagram.Cone.Properties.html#1075" class="Bound">G</a>
<a id="1224" class="Keyword">module</a> <a id="1231" href="Categories.Diagram.Cone.Properties.html#1231" class="Module">CF</a> <a id="1235" class="Symbol">=</a> <a id="1237" href="Categories.Diagram.Cone.html" class="Module">Con</a> <a id="1241" href="Categories.Diagram.Cone.Properties.html#1057" class="Bound">F</a>
<a id="1247" href="Categories.Diagram.Cone.Properties.html#1247" class="Function">FG</a> <a id="1250" class="Symbol">=</a> <a id="1252" href="Categories.Diagram.Cone.Properties.html#1057" class="Bound">F</a> <a id="1254" href="Categories.Functor.html#747" class="Function Operator">∘F</a> <a id="1257" href="Categories.Diagram.Cone.Properties.html#1075" class="Bound">G</a>
<a id="1263" class="Keyword">module</a> <a id="1270" href="Categories.Diagram.Cone.Properties.html#1270" class="Module">CFG</a> <a id="1274" class="Symbol">=</a> <a id="1276" href="Categories.Diagram.Cone.html" class="Module">Con</a> <a id="1280" href="Categories.Diagram.Cone.Properties.html#1247" class="Function">FG</a>
<a id="1286" href="Categories.Diagram.Cone.Properties.html#1286" class="Function">F-map-Coneʳ</a> <a id="1298" class="Symbol">:</a> <a id="1300" href="Categories.Diagram.Cone.html#526" class="Record">CF.Cone</a> <a id="1308" class="Symbol">→</a> <a id="1310" href="Categories.Diagram.Cone.html#526" class="Record">CFG.Cone</a>
<a id="1321" href="Categories.Diagram.Cone.Properties.html#1286" class="Function">F-map-Coneʳ</a> <a id="1333" href="Categories.Diagram.Cone.Properties.html#1333" class="Bound">K</a> <a id="1335" class="Symbol">=</a> <a id="1337" class="Keyword">record</a>
<a id="1348" class="Symbol">{</a> <a id="1350" href="Categories.Diagram.Cone.html#592" class="Field">apex</a> <a id="1355" class="Symbol">=</a> <a id="1357" class="Keyword">record</a>
<a id="1370" class="Symbol">{</a> <a id="1372" href="Categories.Diagram.Cone.html#415" class="Field">ψ</a> <a id="1380" class="Symbol">=</a> <a id="1382" class="Symbol">λ</a> <a id="1384" href="Categories.Diagram.Cone.Properties.html#1384" class="Bound">j</a> <a id="1386" class="Symbol">→</a> <a id="1388" href="Categories.Diagram.Cone.html#415" class="Function">ψ</a> <a id="1390" class="Symbol">(</a><a id="1391" href="Categories.Functor.Core.html#432" class="Field">G.F₀</a> <a id="1396" href="Categories.Diagram.Cone.Properties.html#1384" class="Bound">j</a><a id="1397" class="Symbol">)</a>
<a id="1405" class="Symbol">;</a> <a id="1407" href="Categories.Diagram.Cone.html#463" class="Field">commute</a> <a id="1415" class="Symbol">=</a> <a id="1417" class="Symbol">λ</a> <a id="1419" href="Categories.Diagram.Cone.Properties.html#1419" class="Bound">f</a> <a id="1421" class="Symbol">→</a> <a id="1423" href="Categories.Diagram.Cone.html#463" class="Function">commute</a> <a id="1431" class="Symbol">(</a><a id="1432" href="Categories.Functor.Core.html#455" class="Field">G.F₁</a> <a id="1437" href="Categories.Diagram.Cone.Properties.html#1419" class="Bound">f</a><a id="1438" class="Symbol">)</a>
<a id="1446" class="Symbol">}</a>
<a id="1452" class="Symbol">}</a>
<a id="1458" class="Keyword">where</a> <a id="1464" class="Keyword">open</a> <a id="1469" href="Categories.Diagram.Cone.html#526" class="Module">CF.Cone</a> <a id="1477" href="Categories.Diagram.Cone.Properties.html#1333" class="Bound">K</a>
<a id="1482" href="Categories.Diagram.Cone.Properties.html#1482" class="Function">F-map-Cone⇒ʳ</a> <a id="1495" class="Symbol">:</a> <a id="1497" class="Symbol">∀</a> <a id="1499" class="Symbol">{</a><a id="1500" href="Categories.Diagram.Cone.Properties.html#1500" class="Bound">K</a> <a id="1502" href="Categories.Diagram.Cone.Properties.html#1502" class="Bound">K′</a><a id="1504" class="Symbol">}</a> <a id="1506" class="Symbol">(</a><a id="1507" href="Categories.Diagram.Cone.Properties.html#1507" class="Bound">f</a> <a id="1509" class="Symbol">:</a> <a id="1511" href="Categories.Diagram.Cone.html#660" class="Record">CF.Cone⇒</a> <a id="1520" href="Categories.Diagram.Cone.Properties.html#1500" class="Bound">K</a> <a id="1522" href="Categories.Diagram.Cone.Properties.html#1502" class="Bound">K′</a><a id="1524" class="Symbol">)</a> <a id="1526" class="Symbol">→</a> <a id="1528" href="Categories.Diagram.Cone.html#660" class="Record">CFG.Cone⇒</a> <a id="1538" class="Symbol">(</a><a id="1539" href="Categories.Diagram.Cone.Properties.html#1286" class="Function">F-map-Coneʳ</a> <a id="1551" href="Categories.Diagram.Cone.Properties.html#1500" class="Bound">K</a><a id="1552" class="Symbol">)</a> <a id="1554" class="Symbol">(</a><a id="1555" href="Categories.Diagram.Cone.Properties.html#1286" class="Function">F-map-Coneʳ</a> <a id="1567" href="Categories.Diagram.Cone.Properties.html#1502" class="Bound">K′</a><a id="1569" class="Symbol">)</a>
<a id="1573" href="Categories.Diagram.Cone.Properties.html#1482" class="Function">F-map-Cone⇒ʳ</a> <a id="1586" href="Categories.Diagram.Cone.Properties.html#1586" class="Bound">f</a> <a id="1588" class="Symbol">=</a> <a id="1590" class="Keyword">record</a>
<a id="1601" class="Symbol">{</a> <a id="1603" href="Categories.Diagram.Cone.html#717" class="Field">arr</a> <a id="1611" class="Symbol">=</a> <a id="1613" href="Categories.Diagram.Cone.html#717" class="Field">arr</a>
<a id="1621" class="Symbol">;</a> <a id="1623" href="Categories.Diagram.Cone.html#742" class="Field">commute</a> <a id="1631" class="Symbol">=</a> <a id="1633" href="Categories.Diagram.Cone.html#742" class="Field">commute</a>
<a id="1645" class="Symbol">}</a>
<a id="1651" class="Keyword">where</a> <a id="1657" class="Keyword">open</a> <a id="1662" href="Categories.Diagram.Cone.html#660" class="Module">CF.Cone⇒</a> <a id="1671" href="Categories.Diagram.Cone.Properties.html#1586" class="Bound">f</a>
<a id="1674" class="Keyword">module</a> <a id="1681" href="Categories.Diagram.Cone.Properties.html#1681" class="Module">_</a> <a id="1683" class="Symbol">{</a><a id="1684" href="Categories.Diagram.Cone.Properties.html#1684" class="Bound">F</a> <a id="1686" href="Categories.Diagram.Cone.Properties.html#1686" class="Bound">G</a> <a id="1688" class="Symbol">:</a> <a id="1690" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1698" href="Categories.Diagram.Cone.Properties.html#382" class="Generalizable">J</a> <a id="1700" href="Categories.Diagram.Cone.Properties.html#378" class="Generalizable">C</a><a id="1701" class="Symbol">}</a> <a id="1703" class="Symbol">(</a><a id="1704" href="Categories.Diagram.Cone.Properties.html#1704" class="Bound">α</a> <a id="1706" class="Symbol">:</a> <a id="1708" href="Categories.NaturalTransformation.Core.html#466" class="Record">NaturalTransformation</a> <a id="1730" href="Categories.Diagram.Cone.Properties.html#1684" class="Bound">F</a> <a id="1732" href="Categories.Diagram.Cone.Properties.html#1686" class="Bound">G</a><a id="1733" class="Symbol">)</a> <a id="1735" class="Keyword">where</a>
<a id="1743" class="Keyword">private</a>
<a id="1755" class="Keyword">module</a> <a id="1762" href="Categories.Diagram.Cone.Properties.html#1762" class="Module">C</a> <a id="1765" class="Symbol">=</a> <a id="1767" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="1776" href="Categories.Diagram.Cone.Properties.html#1700" class="Bound">C</a>
<a id="1782" class="Keyword">module</a> <a id="1789" href="Categories.Diagram.Cone.Properties.html#1789" class="Module">J</a> <a id="1792" class="Symbol">=</a> <a id="1794" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="1803" href="Categories.Diagram.Cone.Properties.html#1698" class="Bound">J</a>
<a id="1809" class="Keyword">module</a> <a id="1816" href="Categories.Diagram.Cone.Properties.html#1816" class="Module">F</a> <a id="1819" class="Symbol">=</a> <a id="1821" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="1829" href="Categories.Diagram.Cone.Properties.html#1684" class="Bound">F</a>
<a id="1835" class="Keyword">module</a> <a id="1842" href="Categories.Diagram.Cone.Properties.html#1842" class="Module">G</a> <a id="1845" class="Symbol">=</a> <a id="1847" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="1855" href="Categories.Diagram.Cone.Properties.html#1686" class="Bound">G</a>
<a id="1861" class="Keyword">module</a> <a id="1868" href="Categories.Diagram.Cone.Properties.html#1868" class="Module">α</a> <a id="1871" class="Symbol">=</a> <a id="1873" href="Categories.NaturalTransformation.Core.html#466" class="Module">NaturalTransformation</a> <a id="1895" href="Categories.Diagram.Cone.Properties.html#1704" class="Bound">α</a>
<a id="1901" class="Keyword">module</a> <a id="1908" href="Categories.Diagram.Cone.Properties.html#1908" class="Module">CF</a> <a id="1911" class="Symbol">=</a> <a id="1913" href="Categories.Diagram.Cone.html" class="Module">Con</a> <a id="1917" href="Categories.Diagram.Cone.Properties.html#1684" class="Bound">F</a>
<a id="1923" class="Keyword">module</a> <a id="1930" href="Categories.Diagram.Cone.Properties.html#1930" class="Module">CG</a> <a id="1933" class="Symbol">=</a> <a id="1935" href="Categories.Diagram.Cone.html" class="Module">Con</a> <a id="1939" href="Categories.Diagram.Cone.Properties.html#1686" class="Bound">G</a>
<a id="1945" class="Keyword">open</a> <a id="1950" href="Categories.Diagram.Cone.Properties.html#1762" class="Module">C</a>
<a id="1956" class="Keyword">open</a> <a id="1961" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
<a id="1978" class="Keyword">open</a> <a id="1983" href="Categories.Morphism.Reasoning.html" class="Module">MR</a> <a id="1986" href="Categories.Diagram.Cone.Properties.html#1700" class="Bound">C</a>
<a id="1991" href="Categories.Diagram.Cone.Properties.html#1991" class="Function">nat-map-Cone</a> <a id="2004" class="Symbol">:</a> <a id="2006" href="Categories.Diagram.Cone.html#526" class="Record">CF.Cone</a> <a id="2014" class="Symbol">→</a> <a id="2016" href="Categories.Diagram.Cone.html#526" class="Record">CG.Cone</a>
<a id="2026" href="Categories.Diagram.Cone.Properties.html#1991" class="Function">nat-map-Cone</a> <a id="2039" href="Categories.Diagram.Cone.Properties.html#2039" class="Bound">K</a> <a id="2041" class="Symbol">=</a> <a id="2043" class="Keyword">record</a>
<a id="2054" class="Symbol">{</a> <a id="2056" href="Categories.Diagram.Cone.html#592" class="Field">apex</a> <a id="2061" class="Symbol">=</a> <a id="2063" class="Keyword">record</a>
<a id="2076" class="Symbol">{</a> <a id="2078" href="Categories.Diagram.Cone.html#415" class="Field">ψ</a> <a id="2086" class="Symbol">=</a> <a id="2088" class="Symbol">λ</a> <a id="2090" href="Categories.Diagram.Cone.Properties.html#2090" class="Bound">j</a> <a id="2092" class="Symbol">→</a> <a id="2094" href="Categories.NaturalTransformation.Core.html#783" class="Field">α.η</a> <a id="2098" href="Categories.Diagram.Cone.Properties.html#2090" class="Bound">j</a> <a id="2100" href="Categories.Category.Core.html#656" class="Function Operator">C.∘</a> <a id="2104" href="Categories.Diagram.Cone.html#415" class="Function">ψ</a> <a id="2106" href="Categories.Diagram.Cone.Properties.html#2090" class="Bound">j</a>
<a id="2114" class="Symbol">;</a> <a id="2116" href="Categories.Diagram.Cone.html#463" class="Field">commute</a> <a id="2124" class="Symbol">=</a> <a id="2126" class="Symbol">λ</a> <a id="2128" class="Symbol">{</a><a id="2129" href="Categories.Diagram.Cone.Properties.html#2129" class="Bound">X</a> <a id="2131" href="Categories.Diagram.Cone.Properties.html#2131" class="Bound">Y</a><a id="2132" class="Symbol">}</a> <a id="2134" href="Categories.Diagram.Cone.Properties.html#2134" class="Bound">f</a> <a id="2136" class="Symbol">→</a> <a id="2138" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="2152" href="Categories.Functor.Core.html#455" class="Function">G.F₁</a> <a id="2157" href="Categories.Diagram.Cone.Properties.html#2134" class="Bound">f</a> <a id="2159" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2161" href="Categories.NaturalTransformation.Core.html#783" class="Field">α.η</a> <a id="2165" href="Categories.Diagram.Cone.Properties.html#2129" class="Bound">X</a> <a id="2167" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2169" href="Categories.Diagram.Cone.html#415" class="Function">ψ</a> <a id="2171" href="Categories.Diagram.Cone.Properties.html#2129" class="Bound">X</a> <a id="2173" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">≈˘⟨</a> <a id="2177" href="Categories.Morphism.Reasoning.Core.html#2485" class="Function">pushˡ</a> <a id="2183" class="Symbol">(</a><a id="2184" href="Categories.NaturalTransformation.Core.html#827" class="Field">α.commute</a> <a id="2194" href="Categories.Diagram.Cone.Properties.html#2134" class="Bound">f</a><a id="2195" class="Symbol">)</a> <a id="2197" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">⟩</a>
<a id="2207" class="Symbol">(</a><a id="2208" href="Categories.NaturalTransformation.Core.html#783" class="Field">α.η</a> <a id="2212" href="Categories.Diagram.Cone.Properties.html#2131" class="Bound">Y</a> <a id="2214" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2216" href="Categories.Functor.Core.html#455" class="Function">F.F₁</a> <a id="2221" href="Categories.Diagram.Cone.Properties.html#2134" class="Bound">f</a><a id="2222" class="Symbol">)</a> <a id="2224" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2226" href="Categories.Diagram.Cone.html#415" class="Function">ψ</a> <a id="2228" href="Categories.Diagram.Cone.Properties.html#2129" class="Bound">X</a> <a id="2230" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="2233" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="2239" class="Symbol">(</a><a id="2240" href="Categories.Diagram.Cone.html#463" class="Function">commute</a> <a id="2248" href="Categories.Diagram.Cone.Properties.html#2134" class="Bound">f</a><a id="2249" class="Symbol">)</a> <a id="2251" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="2261" href="Categories.NaturalTransformation.Core.html#783" class="Field">α.η</a> <a id="2265" href="Categories.Diagram.Cone.Properties.html#2131" class="Bound">Y</a> <a id="2267" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="2269" href="Categories.Diagram.Cone.html#415" class="Function">ψ</a> <a id="2271" href="Categories.Diagram.Cone.Properties.html#2131" class="Bound">Y</a> <a id="2273" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="2281" class="Symbol">}</a>
<a id="2287" class="Symbol">}</a>
<a id="2293" class="Keyword">where</a> <a id="2299" class="Keyword">open</a> <a id="2304" href="Categories.Diagram.Cone.html#526" class="Module">CF.Cone</a> <a id="2312" href="Categories.Diagram.Cone.Properties.html#2039" class="Bound">K</a>
<a id="2317" href="Categories.Diagram.Cone.Properties.html#2317" class="Function">nat-map-Cone⇒</a> <a id="2331" class="Symbol">:</a> <a id="2333" class="Symbol">∀</a> <a id="2335" class="Symbol">{</a><a id="2336" href="Categories.Diagram.Cone.Properties.html#2336" class="Bound">K</a> <a id="2338" href="Categories.Diagram.Cone.Properties.html#2338" class="Bound">K′</a><a id="2340" class="Symbol">}</a> <a id="2342" class="Symbol">(</a><a id="2343" href="Categories.Diagram.Cone.Properties.html#2343" class="Bound">f</a> <a id="2345" class="Symbol">:</a> <a id="2347" href="Categories.Diagram.Cone.html#660" class="Record">CF.Cone⇒</a> <a id="2356" href="Categories.Diagram.Cone.Properties.html#2336" class="Bound">K</a> <a id="2358" href="Categories.Diagram.Cone.Properties.html#2338" class="Bound">K′</a><a id="2360" class="Symbol">)</a> <a id="2362" class="Symbol">→</a> <a id="2364" href="Categories.Diagram.Cone.html#660" class="Record">CG.Cone⇒</a> <a id="2373" class="Symbol">(</a><a id="2374" href="Categories.Diagram.Cone.Properties.html#1991" class="Function">nat-map-Cone</a> <a id="2387" href="Categories.Diagram.Cone.Properties.html#2336" class="Bound">K</a><a id="2388" class="Symbol">)</a> <a id="2390" class="Symbol">(</a><a id="2391" href="Categories.Diagram.Cone.Properties.html#1991" class="Function">nat-map-Cone</a> <a id="2404" href="Categories.Diagram.Cone.Properties.html#2338" class="Bound">K′</a><a id="2406" class="Symbol">)</a>
<a id="2410" href="Categories.Diagram.Cone.Properties.html#2317" class="Function">nat-map-Cone⇒</a> <a id="2424" class="Symbol">{</a><a id="2425" href="Categories.Diagram.Cone.Properties.html#2425" class="Bound">K</a><a id="2426" class="Symbol">}</a> <a id="2428" class="Symbol">{</a><a id="2429" href="Categories.Diagram.Cone.Properties.html#2429" class="Bound">K′</a><a id="2431" class="Symbol">}</a> <a id="2433" href="Categories.Diagram.Cone.Properties.html#2433" class="Bound">f</a> <a id="2435" class="Symbol">=</a> <a id="2437" class="Keyword">record</a>
<a id="2448" class="Symbol">{</a> <a id="2450" href="Categories.Diagram.Cone.html#717" class="Field">arr</a> <a id="2458" class="Symbol">=</a> <a id="2460" href="Categories.Diagram.Cone.html#717" class="Field">arr</a>
<a id="2468" class="Symbol">;</a> <a id="2470" href="Categories.Diagram.Cone.html#742" class="Field">commute</a> <a id="2478" class="Symbol">=</a> <a id="2480" href="Categories.Morphism.Reasoning.Core.html#1914" class="Function">pullʳ</a> <a id="2486" href="Categories.Diagram.Cone.html#742" class="Field">commute</a>
<a id="2498" class="Symbol">}</a>
<a id="2504" class="Keyword">where</a> <a id="2510" class="Keyword">open</a> <a id="2515" href="Categories.Diagram.Cone.html#660" class="Module">CF.Cone⇒</a> <a id="2524" href="Categories.Diagram.Cone.Properties.html#2433" class="Bound">f</a>
</pre></body></html>
Reference in a new issue View git blame Copy permalink