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.Object.Terminal.html

77 lines
28 KiB
HTML
Raw Normal View History

Changed out to public
2023-08-19 16:11:22 +02:00
<!DOCTYPE HTML>
<html><head><meta charset="utf-8"><title>Categories.Object.Terminal</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">open</a> <a id="41" class="Keyword">import</a> <a id="48" href="Categories.Category.html" class="Module">Categories.Category</a>
<a id="69" class="Comment">-- Definition of Terminal object and some properties</a>
<a id="123" class="Keyword">module</a> <a id="130" href="Categories.Object.Terminal.html" class="Module">Categories.Object.Terminal</a> <a id="157" class="Symbol">{</a><a id="158" href="Categories.Object.Terminal.html#158" class="Bound">o</a> <a id="160" href="Categories.Object.Terminal.html#160" class="Bound">ℓ</a> <a id="162" href="Categories.Object.Terminal.html#162" class="Bound">e</a><a id="163" class="Symbol">}</a> <a id="165" class="Symbol">(</a><a id="166" href="Categories.Object.Terminal.html#166" class="Bound">C</a> <a id="168" class="Symbol">:</a> <a id="170" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="179" href="Categories.Object.Terminal.html#158" class="Bound">o</a> <a id="181" href="Categories.Object.Terminal.html#160" class="Bound">ℓ</a> <a id="183" href="Categories.Object.Terminal.html#162" class="Bound">e</a><a id="184" class="Symbol">)</a> <a id="186" class="Keyword">where</a>
<a id="193" class="Keyword">open</a> <a id="198" class="Keyword">import</a> <a id="205" href="Level.html" class="Module">Level</a>
<a id="212" class="Keyword">open</a> <a id="217" class="Keyword">import</a> <a id="224" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="240" class="Keyword">using</a> <a id="246" class="Symbol">(</a><a id="247" href="Relation.Binary.Structures.html#1531" class="Record">IsEquivalence</a><a id="260" class="Symbol">;</a> <a id="262" href="Relation.Binary.Bundles.html#1018" class="Record">Setoid</a><a id="268" class="Symbol">)</a>
<a id="270" class="Keyword">open</a> <a id="275" class="Keyword">import</a> <a id="282" href="Relation.Binary.PropositionalEquality.html" class="Module">Relation.Binary.PropositionalEquality</a> <a id="320" class="Symbol">as</a> <a id="323" class="Module">≡</a> <a id="325" class="Keyword">using</a> <a id="331" class="Symbol">(</a><a id="332" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">_≡_</a><a id="335" class="Symbol">)</a>
<a id="338" class="Keyword">open</a> <a id="343" class="Keyword">import</a> <a id="350" href="Categories.Morphism.html" class="Module">Categories.Morphism</a> <a id="370" href="Categories.Object.Terminal.html#166" class="Bound">C</a>
<a id="372" class="Keyword">open</a> <a id="377" class="Keyword">import</a> <a id="384" href="Categories.Morphism.IsoEquiv.html" class="Module">Categories.Morphism.IsoEquiv</a> <a id="413" href="Categories.Object.Terminal.html#166" class="Bound">C</a> <a id="415" class="Keyword">using</a> <a id="421" class="Symbol">(</a><a id="422" href="Categories.Morphism.IsoEquiv.html#1761" class="Record Operator">_≃_</a><a id="425" class="Symbol">;</a> <a id="427" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞_⌟</a><a id="430" class="Symbol">)</a>
<a id="432" class="Keyword">open</a> <a id="437" class="Keyword">import</a> <a id="444" href="Categories.Morphism.Reasoning.html" class="Module">Categories.Morphism.Reasoning</a> <a id="474" href="Categories.Object.Terminal.html#166" class="Bound">C</a>
<a id="477" class="Keyword">open</a> <a id="482" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="491" href="Categories.Object.Terminal.html#166" class="Bound">C</a>
<a id="493" class="Keyword">open</a> <a id="498" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
<a id="513" class="Keyword">record</a> <a id="IsTerminal"></a><a id="520" href="Categories.Object.Terminal.html#520" class="Record">IsTerminal</a> <a id="531" class="Symbol">(</a><a id="532" href="Categories.Object.Terminal.html#532" class="Bound">⊤</a> <a id="534" class="Symbol">:</a> <a id="536" href="Categories.Category.Core.html#559" class="Field">Obj</a><a id="539" class="Symbol">)</a> <a id="541" class="Symbol">:</a> <a id="543" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="547" class="Symbol">(</a><a id="548" href="Categories.Object.Terminal.html#158" class="Bound">o</a> <a id="550" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="552" href="Categories.Object.Terminal.html#160" class="Bound">ℓ</a> <a id="554" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="556" href="Categories.Object.Terminal.html#162" class="Bound">e</a><a id="557" class="Symbol">)</a> <a id="559" class="Keyword">where</a>
<a id="567" class="Keyword">field</a>
<a id="IsTerminal.!"></a><a id="577" href="Categories.Object.Terminal.html#577" class="Field">!</a> <a id="579" class="Symbol">:</a> <a id="581" class="Symbol">{</a><a id="582" href="Categories.Object.Terminal.html#582" class="Bound">A</a> <a id="584" class="Symbol">:</a> <a id="586" href="Categories.Category.Core.html#559" class="Field">Obj</a><a id="589" class="Symbol">}</a> <a id="591" class="Symbol">→</a> <a id="593" class="Symbol">(</a><a id="594" href="Categories.Object.Terminal.html#582" class="Bound">A</a> <a id="596" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="598" href="Categories.Object.Terminal.html#532" class="Bound">⊤</a><a id="599" class="Symbol">)</a>
<a id="IsTerminal.!-unique"></a><a id="605" href="Categories.Object.Terminal.html#605" class="Field">!-unique</a> <a id="614" class="Symbol">:</a> <a id="616" class="Symbol">∀</a> <a id="618" class="Symbol">{</a><a id="619" href="Categories.Object.Terminal.html#619" class="Bound">A</a><a id="620" class="Symbol">}</a> <a id="622" class="Symbol">→</a> <a id="624" class="Symbol">(</a><a id="625" href="Categories.Object.Terminal.html#625" class="Bound">f</a> <a id="627" class="Symbol">:</a> <a id="629" href="Categories.Object.Terminal.html#619" class="Bound">A</a> <a id="631" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="633" href="Categories.Object.Terminal.html#532" class="Bound">⊤</a><a id="634" class="Symbol">)</a> <a id="636" class="Symbol">→</a> <a id="638" href="Categories.Object.Terminal.html#577" class="Field">!</a> <a id="640" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="642" href="Categories.Object.Terminal.html#625" class="Bound">f</a>
<a id="IsTerminal.!-unique₂"></a><a id="647" href="Categories.Object.Terminal.html#647" class="Function">!-unique₂</a> <a id="657" class="Symbol">:</a> <a id="659" class="Symbol">∀</a> <a id="661" class="Symbol">{</a><a id="662" href="Categories.Object.Terminal.html#662" class="Bound">A</a><a id="663" class="Symbol">}</a> <a id="665" class="Symbol">{</a><a id="666" href="Categories.Object.Terminal.html#666" class="Bound">f</a> <a id="668" href="Categories.Object.Terminal.html#668" class="Bound">g</a> <a id="670" class="Symbol">:</a> <a id="672" href="Categories.Object.Terminal.html#662" class="Bound">A</a> <a id="674" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="676" href="Categories.Object.Terminal.html#532" class="Bound">⊤</a><a id="677" class="Symbol">}</a> <a id="679" class="Symbol">→</a> <a id="681" href="Categories.Object.Terminal.html#666" class="Bound">f</a> <a id="683" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="685" href="Categories.Object.Terminal.html#668" class="Bound">g</a>
<a id="689" href="Categories.Object.Terminal.html#647" class="Function">!-unique₂</a> <a id="699" class="Symbol">{</a><a id="700" href="Categories.Object.Terminal.html#700" class="Bound">A</a><a id="701" class="Symbol">}</a> <a id="703" class="Symbol">{</a><a id="704" href="Categories.Object.Terminal.html#704" class="Bound">f</a><a id="705" class="Symbol">}</a> <a id="707" class="Symbol">{</a><a id="708" href="Categories.Object.Terminal.html#708" class="Bound">g</a><a id="709" class="Symbol">}</a> <a id="711" class="Symbol">=</a> <a id="713" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="723" href="Categories.Object.Terminal.html#704" class="Bound">f</a> <a id="725" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">≈˘⟨</a> <a id="729" href="Categories.Object.Terminal.html#605" class="Field">!-unique</a> <a id="738" href="Categories.Object.Terminal.html#704" class="Bound">f</a> <a id="740" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">⟩</a>
<a id="746" href="Categories.Object.Terminal.html#577" class="Field">!</a> <a id="748" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="751" href="Categories.Object.Terminal.html#605" class="Field">!-unique</a> <a id="760" href="Categories.Object.Terminal.html#708" class="Bound">g</a> <a id="762" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="768" href="Categories.Object.Terminal.html#708" class="Bound">g</a> <a id="770" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="776" class="Keyword">where</a> <a id="782" class="Keyword">open</a> <a id="787" href="Categories.Category.Core.html#2462" class="Module">HomReasoning</a>
<a id="IsTerminal.⊤-id"></a><a id="803" href="Categories.Object.Terminal.html#803" class="Function">⊤-id</a> <a id="808" class="Symbol">:</a> <a id="810" class="Symbol">(</a><a id="811" href="Categories.Object.Terminal.html#811" class="Bound">f</a> <a id="813" class="Symbol">:</a> <a id="815" href="Categories.Object.Terminal.html#532" class="Bound">⊤</a> <a id="817" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="819" href="Categories.Object.Terminal.html#532" class="Bound">⊤</a><a id="820" class="Symbol">)</a> <a id="822" class="Symbol">→</a> <a id="824" href="Categories.Object.Terminal.html#811" class="Bound">f</a> <a id="826" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="828" href="Categories.Category.Core.html#630" class="Field">id</a>
<a id="833" href="Categories.Object.Terminal.html#803" class="Function">⊤-id</a> <a id="838" class="Symbol">_</a> <a id="840" class="Symbol">=</a> <a id="842" href="Categories.Object.Terminal.html#647" class="Function">!-unique₂</a>
<a id="853" class="Keyword">record</a> <a id="Terminal"></a><a id="860" href="Categories.Object.Terminal.html#860" class="Record">Terminal</a> <a id="869" class="Symbol">:</a> <a id="871" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="875" class="Symbol">(</a><a id="876" href="Categories.Object.Terminal.html#158" class="Bound">o</a> <a id="878" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="880" href="Categories.Object.Terminal.html#160" class="Bound">ℓ</a> <a id="882" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="884" href="Categories.Object.Terminal.html#162" class="Bound">e</a><a id="885" class="Symbol">)</a> <a id="887" class="Keyword">where</a>
<a id="895" class="Keyword">field</a>
<a id="Terminal.⊤"></a><a id="905" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="907" class="Symbol">:</a> <a id="909" href="Categories.Category.Core.html#559" class="Field">Obj</a>
<a id="Terminal.⊤-is-terminal"></a><a id="917" href="Categories.Object.Terminal.html#917" class="Field">⊤-is-terminal</a> <a id="931" class="Symbol">:</a> <a id="933" href="Categories.Object.Terminal.html#520" class="Record">IsTerminal</a> <a id="944" href="Categories.Object.Terminal.html#905" class="Field">⊤</a>
<a id="949" class="Keyword">open</a> <a id="954" href="Categories.Object.Terminal.html#520" class="Module">IsTerminal</a> <a id="965" href="Categories.Object.Terminal.html#917" class="Field">⊤-is-terminal</a> <a id="979" class="Keyword">public</a>
<a id="987" class="Keyword">open</a> <a id="992" href="Categories.Object.Terminal.html#860" class="Module">Terminal</a>
<a id="from-⊤-is-Mono"></a><a id="1002" href="Categories.Object.Terminal.html#1002" class="Function">from-⊤-is-Mono</a> <a id="1017" class="Symbol">:</a> <a id="1019" class="Symbol">∀</a> <a id="1021" class="Symbol">{</a><a id="1022" href="Categories.Object.Terminal.html#1022" class="Bound">A</a> <a id="1024" class="Symbol">:</a> <a id="1026" href="Categories.Category.Core.html#559" class="Field">Obj</a><a id="1029" class="Symbol">}</a> <a id="1031" class="Symbol">{</a><a id="1032" href="Categories.Object.Terminal.html#1032" class="Bound">t</a> <a id="1034" class="Symbol">:</a> <a id="1036" href="Categories.Object.Terminal.html#860" class="Record">Terminal</a><a id="1044" class="Symbol">}</a> <a id="1046" class="Symbol">→</a> <a id="1048" class="Symbol">(</a><a id="1049" href="Categories.Object.Terminal.html#1049" class="Bound">f</a> <a id="1051" class="Symbol">:</a> <a id="1053" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="1055" href="Categories.Object.Terminal.html#1032" class="Bound">t</a> <a id="1057" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="1059" href="Categories.Object.Terminal.html#1022" class="Bound">A</a><a id="1060" class="Symbol">)</a> <a id="1062" class="Symbol">→</a> <a id="1064" href="Categories.Morphism.html#488" class="Function">Mono</a> <a id="1069" href="Categories.Object.Terminal.html#1049" class="Bound">f</a>
<a id="1071" href="Categories.Object.Terminal.html#1002" class="Function">from-⊤-is-Mono</a> <a id="1086" class="Symbol">{_}</a> <a id="1090" class="Symbol">{</a><a id="1091" href="Categories.Object.Terminal.html#1091" class="Bound">t</a><a id="1092" class="Symbol">}</a> <a id="1094" class="Symbol">_</a> <a id="1096" class="Symbol">=</a> <a id="1098" class="Symbol">λ</a> <a id="1100" href="Categories.Object.Terminal.html#1100" class="Bound">_</a> <a id="1102" href="Categories.Object.Terminal.html#1102" class="Bound">_</a> <a id="1104" href="Categories.Object.Terminal.html#1104" class="Bound">_</a> <a id="1106" class="Symbol">→</a> <a id="1108" href="Categories.Object.Terminal.html#647" class="Function">!-unique₂</a> <a id="1118" href="Categories.Object.Terminal.html#1091" class="Bound">t</a>
<a id="up-to-iso"></a><a id="1121" href="Categories.Object.Terminal.html#1121" class="Function">up-to-iso</a> <a id="1131" class="Symbol">:</a> <a id="1133" class="Symbol">(</a><a id="1134" href="Categories.Object.Terminal.html#1134" class="Bound">t₁</a> <a id="1137" href="Categories.Object.Terminal.html#1137" class="Bound">t₂</a> <a id="1140" class="Symbol">:</a> <a id="1142" href="Categories.Object.Terminal.html#860" class="Record">Terminal</a><a id="1150" class="Symbol">)</a> <a id="1152" class="Symbol">→</a> <a id="1154" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="1156" href="Categories.Object.Terminal.html#1134" class="Bound">t₁</a> <a id="1159" href="Categories.Morphism.html#1958" class="Record Operator">≅</a> <a id="1161" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="1163" href="Categories.Object.Terminal.html#1137" class="Bound">t₂</a>
<a id="1166" href="Categories.Object.Terminal.html#1121" class="Function">up-to-iso</a> <a id="1176" href="Categories.Object.Terminal.html#1176" class="Bound">t₁</a> <a id="1179" href="Categories.Object.Terminal.html#1179" class="Bound">t₂</a> <a id="1182" class="Symbol">=</a> <a id="1184" class="Keyword">record</a>
<a id="1193" class="Symbol">{</a> <a id="1195" href="Categories.Morphism.html#2006" class="Field">from</a> <a id="1200" class="Symbol">=</a> <a id="1202" href="Categories.Object.Terminal.html#577" class="Function">!</a> <a id="1204" href="Categories.Object.Terminal.html#1179" class="Bound">t₂</a>
<a id="1209" class="Symbol">;</a> <a id="1211" href="Categories.Morphism.html#2023" class="Field">to</a> <a id="1216" class="Symbol">=</a> <a id="1218" href="Categories.Object.Terminal.html#577" class="Function">!</a> <a id="1220" href="Categories.Object.Terminal.html#1176" class="Bound">t₁</a>
<a id="1225" class="Symbol">;</a> <a id="1227" href="Categories.Morphism.html#2040" class="Field">iso</a> <a id="1232" class="Symbol">=</a> <a id="1234" class="Keyword">record</a> <a id="1241" class="Symbol">{</a> <a id="1243" href="Categories.Morphism.html#1586" class="Field">isoˡ</a> <a id="1248" class="Symbol">=</a> <a id="1250" href="Categories.Object.Terminal.html#803" class="Function">⊤-id</a> <a id="1255" href="Categories.Object.Terminal.html#1176" class="Bound">t₁</a> <a id="1258" class="Symbol">_;</a> <a id="1261" href="Categories.Morphism.html#1612" class="Field">isoʳ</a> <a id="1266" class="Symbol">=</a> <a id="1268" href="Categories.Object.Terminal.html#803" class="Function">⊤-id</a> <a id="1273" href="Categories.Object.Terminal.html#1179" class="Bound">t₂</a> <a id="1276" class="Symbol">_</a> <a id="1278" class="Symbol">}</a>
<a id="1282" class="Symbol">}</a>
<a id="transport-by-iso"></a><a id="1285" href="Categories.Object.Terminal.html#1285" class="Function">transport-by-iso</a> <a id="1302" class="Symbol">:</a> <a id="1304" class="Symbol">(</a><a id="1305" href="Categories.Object.Terminal.html#1305" class="Bound">t</a> <a id="1307" class="Symbol">:</a> <a id="1309" href="Categories.Object.Terminal.html#860" class="Record">Terminal</a><a id="1317" class="Symbol">)</a> <a id="1319" class="Symbol">→</a> <a id="1321" class="Symbol">∀</a> <a id="1323" class="Symbol">{</a><a id="1324" href="Categories.Object.Terminal.html#1324" class="Bound">X</a><a id="1325" class="Symbol">}</a> <a id="1327" class="Symbol">→</a> <a id="1329" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="1331" href="Categories.Object.Terminal.html#1305" class="Bound">t</a> <a id="1333" href="Categories.Morphism.html#1958" class="Record Operator">≅</a> <a id="1335" href="Categories.Object.Terminal.html#1324" class="Bound">X</a> <a id="1337" class="Symbol">→</a> <a id="1339" href="Categories.Object.Terminal.html#860" class="Record">Terminal</a>
<a id="1348" href="Categories.Object.Terminal.html#1285" class="Function">transport-by-iso</a> <a id="1365" href="Categories.Object.Terminal.html#1365" class="Bound">t</a> <a id="1367" class="Symbol">{</a><a id="1368" href="Categories.Object.Terminal.html#1368" class="Bound">X</a><a id="1369" class="Symbol">}</a> <a id="1371" href="Categories.Object.Terminal.html#1371" class="Bound">t≅X</a> <a id="1375" class="Symbol">=</a> <a id="1377" class="Keyword">record</a>
<a id="1386" class="Symbol">{</a> <a id="1388" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="1397" class="Symbol">=</a> <a id="1399" href="Categories.Object.Terminal.html#1368" class="Bound">X</a>
<a id="1403" class="Symbol">;</a> <a id="1405" href="Categories.Object.Terminal.html#917" class="Field">⊤-is-terminal</a> <a id="1419" class="Symbol">=</a> <a id="1421" class="Keyword">record</a>
<a id="1432" class="Symbol">{</a> <a id="1434" href="Categories.Object.Terminal.html#577" class="Field">!</a> <a id="1443" class="Symbol">=</a> <a id="1445" href="Categories.Morphism.html#2006" class="Field">from</a> <a id="1450" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1452" href="Categories.Object.Terminal.html#577" class="Function">!</a> <a id="1454" href="Categories.Object.Terminal.html#1365" class="Bound">t</a>
<a id="1460" class="Symbol">;</a> <a id="1462" href="Categories.Object.Terminal.html#605" class="Field">!-unique</a> <a id="1471" class="Symbol">=</a> <a id="1473" class="Symbol">λ</a> <a id="1475" href="Categories.Object.Terminal.html#1475" class="Bound">h</a> <a id="1477" class="Symbol">→</a> <a id="1479" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="1491" href="Categories.Morphism.html#2006" class="Field">from</a> <a id="1496" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1498" href="Categories.Object.Terminal.html#577" class="Function">!</a> <a id="1500" href="Categories.Object.Terminal.html#1365" class="Bound">t</a> <a id="1506" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1509" href="Categories.Category.Core.html#2734" class="Function Operator">refl⟩∘⟨</a> <a id="1517" href="Categories.Object.Terminal.html#605" class="Function">!-unique</a> <a id="1526" href="Categories.Object.Terminal.html#1365" class="Bound">t</a> <a id="1528" class="Symbol">(</a><a id="1529" href="Categories.Morphism.html#2023" class="Field">to</a> <a id="1532" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1534" href="Categories.Object.Terminal.html#1475" class="Bound">h</a><a id="1535" class="Symbol">)</a> <a id="1538" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="1546" href="Categories.Morphism.html#2006" class="Field">from</a> <a id="1551" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1553" href="Categories.Morphism.html#2023" class="Field">to</a> <a id="1556" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1558" href="Categories.Object.Terminal.html#1475" class="Bound">h</a> <a id="1561" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1564" href="Categories.Morphism.Reasoning.Core.html#6851" class="Function">cancelˡ</a> <a id="1572" href="Categories.Morphism.html#1612" class="Function">isoʳ</a> <a id="1577" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="1585" href="Categories.Object.Terminal.html#1475" class="Bound">h</a> <a id="1600" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="1606" class="Symbol">}</a>
<a id="1610" class="Symbol">}</a>
<a id="1614" class="Keyword">where</a> <a id="1620" class="Keyword">open</a> <a id="1625" href="Categories.Morphism.html#1958" class="Module Operator">_≅_</a> <a id="1629" href="Categories.Object.Terminal.html#1371" class="Bound">t≅X</a>
<a id="up-to-iso-unique"></a><a id="1634" href="Categories.Object.Terminal.html#1634" class="Function">up-to-iso-unique</a> <a id="1651" class="Symbol">:</a> <a id="1653" class="Symbol">∀</a> <a id="1655" href="Categories.Object.Terminal.html#1655" class="Bound">t</a> <a id="1657" href="Categories.Object.Terminal.html#1657" class="Bound">t′</a> <a id="1660" class="Symbol">→</a> <a id="1662" class="Symbol">(</a><a id="1663" href="Categories.Object.Terminal.html#1663" class="Bound">i</a> <a id="1665" class="Symbol">:</a> <a id="1667" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="1669" href="Categories.Object.Terminal.html#1655" class="Bound">t</a> <a id="1671" href="Categories.Morphism.html#1958" class="Record Operator">≅</a> <a id="1673" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="1675" href="Categories.Object.Terminal.html#1657" class="Bound">t′</a><a id="1677" class="Symbol">)</a> <a id="1679" class="Symbol">→</a> <a id="1681" href="Categories.Object.Terminal.html#1121" class="Function">up-to-iso</a> <a id="1691" href="Categories.Object.Terminal.html#1655" class="Bound">t</a> <a id="1693" href="Categories.Object.Terminal.html#1657" class="Bound">t′</a> <a id="1696" href="Categories.Morphism.IsoEquiv.html#1761" class="Record Operator">≃</a> <a id="1698" href="Categories.Object.Terminal.html#1663" class="Bound">i</a>
<a id="1700" href="Categories.Object.Terminal.html#1634" class="Function">up-to-iso-unique</a> <a id="1717" href="Categories.Object.Terminal.html#1717" class="Bound">t</a> <a id="1719" href="Categories.Object.Terminal.html#1719" class="Bound">t′</a> <a id="1722" href="Categories.Object.Terminal.html#1722" class="Bound">i</a> <a id="1724" class="Symbol">=</a> <a id="1726" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌞</a> <a id="1728" href="Categories.Object.Terminal.html#605" class="Function">!-unique</a> <a id="1737" href="Categories.Object.Terminal.html#1719" class="Bound">t′</a> <a id="1740" class="Symbol">_</a> <a id="1742" href="Categories.Morphism.IsoEquiv.html#1807" class="InductiveConstructor Operator">⌟</a>
<a id="up-to-iso-invˡ"></a><a id="1745" href="Categories.Object.Terminal.html#1745" class="Function">up-to-iso-invˡ</a> <a id="1760" class="Symbol">:</a> <a id="1762" class="Symbol">∀</a> <a id="1764" class="Symbol">{</a><a id="1765" href="Categories.Object.Terminal.html#1765" class="Bound">t</a> <a id="1767" href="Categories.Object.Terminal.html#1767" class="Bound">X</a><a id="1768" class="Symbol">}</a> <a id="1770" class="Symbol">{</a><a id="1771" href="Categories.Object.Terminal.html#1771" class="Bound">i</a> <a id="1773" class="Symbol">:</a> <a id="1775" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="1777" href="Categories.Object.Terminal.html#1765" class="Bound">t</a> <a id="1779" href="Categories.Morphism.html#1958" class="Record Operator">≅</a> <a id="1781" href="Categories.Object.Terminal.html#1767" class="Bound">X</a><a id="1782" class="Symbol">}</a> <a id="1784" class="Symbol">→</a> <a id="1786" href="Categories.Object.Terminal.html#1121" class="Function">up-to-iso</a> <a id="1796" href="Categories.Object.Terminal.html#1765" class="Bound">t</a> <a id="1798" class="Symbol">(</a><a id="1799" href="Categories.Object.Terminal.html#1285" class="Function">transport-by-iso</a> <a id="1816" href="Categories.Object.Terminal.html#1765" class="Bound">t</a> <a id="1818" href="Categories.Object.Terminal.html#1771" class="Bound">i</a><a id="1819" class="Symbol">)</a> <a id="1821" href="Categories.Morphism.IsoEquiv.html#1761" class="Record Operator">≃</a> <a id="1823" href="Categories.Object.Terminal.html#1771" class="Bound">i</a>
<a id="1825" href="Categories.Object.Terminal.html#1745" class="Function">up-to-iso-invˡ</a> <a id="1840" class="Symbol">{</a><a id="1841" href="Categories.Object.Terminal.html#1841" class="Bound">t</a><a id="1842" class="Symbol">}</a> <a id="1844" class="Symbol">{</a><a id="1845" class="Argument">i</a> <a id="1847" class="Symbol">=</a> <a id="1849" href="Categories.Object.Terminal.html#1849" class="Bound">i</a><a id="1850" class="Symbol">}</a> <a id="1852" class="Symbol">=</a> <a id="1854" href="Categories.Object.Terminal.html#1634" class="Function">up-to-iso-unique</a> <a id="1871" href="Categories.Object.Terminal.html#1841" class="Bound">t</a> <a id="1873" class="Symbol">(</a><a id="1874" href="Categories.Object.Terminal.html#1285" class="Function">transport-by-iso</a> <a id="1891" href="Categories.Object.Terminal.html#1841" class="Bound">t</a> <a id="1893" href="Categories.Object.Terminal.html#1849" class="Bound">i</a><a id="1894" class="Symbol">)</a> <a id="1896" href="Categories.Object.Terminal.html#1849" class="Bound">i</a>
<a id="up-to-iso-invʳ"></a><a id="1899" href="Categories.Object.Terminal.html#1899" class="Function">up-to-iso-invʳ</a> <a id="1914" class="Symbol">:</a> <a id="1916" class="Symbol">∀</a> <a id="1918" class="Symbol">{</a><a id="1919" href="Categories.Object.Terminal.html#1919" class="Bound">t</a> <a id="1921" href="Categories.Object.Terminal.html#1921" class="Bound">t′</a><a id="1923" class="Symbol">}</a> <a id="1925" class="Symbol">→</a> <a id="1927" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="1929" class="Symbol">(</a><a id="1930" href="Categories.Object.Terminal.html#1285" class="Function">transport-by-iso</a> <a id="1947" href="Categories.Object.Terminal.html#1919" class="Bound">t</a> <a id="1949" class="Symbol">(</a><a id="1950" href="Categories.Object.Terminal.html#1121" class="Function">up-to-iso</a> <a id="1960" href="Categories.Object.Terminal.html#1919" class="Bound">t</a> <a id="1962" href="Categories.Object.Terminal.html#1921" class="Bound">t′</a><a id="1964" class="Symbol">))</a> <a id="1967" href="Agda.Builtin.Equality.html#133" class="Datatype Operator">≡</a> <a id="1969" href="Categories.Object.Terminal.html#905" class="Field">⊤</a> <a id="1971" href="Categories.Object.Terminal.html#1921" class="Bound">t′</a>
<a id="1974" href="Categories.Object.Terminal.html#1899" class="Function">up-to-iso-invʳ</a> <a id="1989" class="Symbol">{</a><a id="1990" href="Categories.Object.Terminal.html#1990" class="Bound">t</a><a id="1991" class="Symbol">}</a> <a id="1993" class="Symbol">{</a><a id="1994" href="Categories.Object.Terminal.html#1994" class="Bound">t′</a><a id="1996" class="Symbol">}</a> <a id="1998" class="Symbol">=</a> <a id="2000" href="Agda.Builtin.Equality.html#190" class="InductiveConstructor">≡.refl</a>
</pre></body></html>
Reference in a new issue Copy permalink