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/Algebra.Morphism.Definitions.html

48 lines
No EOL
11 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>Algebra.Morphism.Definitions</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Comment">------------------------------------------------------------------------</a>
<a id="74" class="Comment">-- The Agda standard library</a>
<a id="103" class="Comment">--</a>
<a id="106" class="Comment">-- Basic definitions for morphisms between algebraic structures</a>
<a id="170" class="Comment">------------------------------------------------------------------------</a>
<a id="244" class="Symbol">{-#</a> <a id="248" class="Keyword">OPTIONS</a> <a id="256" class="Pragma">--cubical-compatible</a> <a id="277" class="Pragma">--safe</a> <a id="284" class="Symbol">#-}</a>
<a id="289" class="Keyword">open</a> <a id="294" class="Keyword">import</a> <a id="301" href="Relation.Binary.Core.html" class="Module">Relation.Binary.Core</a>
<a id="323" class="Keyword">module</a> <a id="330" href="Algebra.Morphism.Definitions.html" class="Module">Algebra.Morphism.Definitions</a>
<a id="361" class="Symbol">{</a><a id="362" href="Algebra.Morphism.Definitions.html#362" class="Bound">a</a><a id="363" class="Symbol">}</a> <a id="365" class="Symbol">(</a><a id="366" href="Algebra.Morphism.Definitions.html#366" class="Bound">A</a> <a id="368" class="Symbol">:</a> <a id="370" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="374" href="Algebra.Morphism.Definitions.html#362" class="Bound">a</a><a id="375" class="Symbol">)</a> <a id="381" class="Comment">-- The domain of the morphism</a>
<a id="413" class="Symbol">{</a><a id="414" href="Algebra.Morphism.Definitions.html#414" class="Bound">b</a><a id="415" class="Symbol">}</a> <a id="417" class="Symbol">(</a><a id="418" href="Algebra.Morphism.Definitions.html#418" class="Bound">B</a> <a id="420" class="Symbol">:</a> <a id="422" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="426" href="Algebra.Morphism.Definitions.html#414" class="Bound">b</a><a id="427" class="Symbol">)</a> <a id="433" class="Comment">-- The codomain of the morphism</a>
<a id="467" class="Symbol">{</a><a id="468" href="Algebra.Morphism.Definitions.html#468" class="Bound">ℓ</a><a id="469" class="Symbol">}</a> <a id="471" class="Symbol">(</a><a id="472" href="Algebra.Morphism.Definitions.html#472" class="Bound Operator">_≈_</a> <a id="476" class="Symbol">:</a> <a id="478" href="Relation.Binary.Core.html#891" class="Function">Rel</a> <a id="482" href="Algebra.Morphism.Definitions.html#418" class="Bound">B</a> <a id="484" href="Algebra.Morphism.Definitions.html#468" class="Bound">ℓ</a><a id="485" class="Symbol">)</a> <a id="488" class="Comment">-- The equality relation over the codomain</a>
<a id="533" class="Keyword">where</a>
<a id="540" class="Keyword">open</a> <a id="545" class="Keyword">import</a> <a id="552" href="Algebra.Core.html" class="Module">Algebra.Core</a>
<a id="567" class="Keyword">using</a> <a id="573" class="Symbol">(</a><a id="574" href="Algebra.Core.html#484" class="Function">Op₁</a><a id="577" class="Symbol">;</a> <a id="579" href="Algebra.Core.html#527" class="Function">Op₂</a><a id="582" class="Symbol">)</a>
<a id="585" class="Comment">------------------------------------------------------------------------</a>
<a id="658" class="Comment">-- Basic definitions</a>
<a id="Homomorphic₀"></a><a id="680" href="Algebra.Morphism.Definitions.html#680" class="Function">Homomorphic₀</a> <a id="693" class="Symbol">:</a> <a id="695" class="Symbol">(</a><a id="696" href="Algebra.Morphism.Definitions.html#366" class="Bound">A</a> <a id="698" class="Symbol">→</a> <a id="700" href="Algebra.Morphism.Definitions.html#418" class="Bound">B</a><a id="701" class="Symbol">)</a> <a id="703" class="Symbol">→</a> <a id="705" href="Algebra.Morphism.Definitions.html#366" class="Bound">A</a> <a id="707" class="Symbol">→</a> <a id="709" href="Algebra.Morphism.Definitions.html#418" class="Bound">B</a> <a id="711" class="Symbol">→</a> <a id="713" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="717" class="Symbol">_</a>
<a id="719" href="Algebra.Morphism.Definitions.html#680" class="Function">Homomorphic₀</a> <a id="732" href="Algebra.Morphism.Definitions.html#732" class="Bound Operator">⟦_⟧</a> <a id="736" href="Algebra.Morphism.Definitions.html#736" class="Bound">∙</a> <a id="738" href="Algebra.Morphism.Definitions.html#738" class="Bound">∘</a> <a id="740" class="Symbol">=</a> <a id="742" href="Algebra.Morphism.Definitions.html#732" class="Bound Operator">⟦</a> <a id="744" href="Algebra.Morphism.Definitions.html#736" class="Bound">∙</a> <a id="746" href="Algebra.Morphism.Definitions.html#732" class="Bound Operator">⟧</a> <a id="748" href="Algebra.Morphism.Definitions.html#472" class="Bound Operator">≈</a> <a id="750" href="Algebra.Morphism.Definitions.html#738" class="Bound">∘</a>
<a id="Homomorphic₁"></a><a id="753" href="Algebra.Morphism.Definitions.html#753" class="Function">Homomorphic₁</a> <a id="766" class="Symbol">:</a> <a id="768" class="Symbol">(</a><a id="769" href="Algebra.Morphism.Definitions.html#366" class="Bound">A</a> <a id="771" class="Symbol">→</a> <a id="773" href="Algebra.Morphism.Definitions.html#418" class="Bound">B</a><a id="774" class="Symbol">)</a> <a id="776" class="Symbol">→</a> <a id="778" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="782" href="Algebra.Morphism.Definitions.html#366" class="Bound">A</a> <a id="784" class="Symbol">→</a> <a id="786" href="Algebra.Core.html#484" class="Function">Op₁</a> <a id="790" href="Algebra.Morphism.Definitions.html#418" class="Bound">B</a> <a id="792" class="Symbol">→</a> <a id="794" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="798" class="Symbol">_</a>
<a id="800" href="Algebra.Morphism.Definitions.html#753" class="Function">Homomorphic₁</a> <a id="813" href="Algebra.Morphism.Definitions.html#813" class="Bound Operator">⟦_⟧</a> <a id="817" href="Algebra.Morphism.Definitions.html#817" class="Bound Operator">∙_</a> <a id="820" href="Algebra.Morphism.Definitions.html#820" class="Bound Operator">∘_</a> <a id="823" class="Symbol">=</a> <a id="825" class="Symbol">∀</a> <a id="827" href="Algebra.Morphism.Definitions.html#827" class="Bound">x</a> <a id="829" class="Symbol">→</a> <a id="831" href="Algebra.Morphism.Definitions.html#813" class="Bound Operator">⟦</a> <a id="833" href="Algebra.Morphism.Definitions.html#817" class="Bound Operator">∙</a> <a id="835" href="Algebra.Morphism.Definitions.html#827" class="Bound">x</a> <a id="837" href="Algebra.Morphism.Definitions.html#813" class="Bound Operator">⟧</a> <a id="839" href="Algebra.Morphism.Definitions.html#472" class="Bound Operator">≈</a> <a id="841" class="Symbol">(</a><a id="842" href="Algebra.Morphism.Definitions.html#820" class="Bound Operator">∘</a> <a id="844" href="Algebra.Morphism.Definitions.html#813" class="Bound Operator">⟦</a> <a id="846" href="Algebra.Morphism.Definitions.html#827" class="Bound">x</a> <a id="848" href="Algebra.Morphism.Definitions.html#813" class="Bound Operator">⟧</a><a id="849" class="Symbol">)</a>
<a id="Homomorphic₂"></a><a id="852" href="Algebra.Morphism.Definitions.html#852" class="Function">Homomorphic₂</a> <a id="865" class="Symbol">:</a> <a id="867" class="Symbol">(</a><a id="868" href="Algebra.Morphism.Definitions.html#366" class="Bound">A</a> <a id="870" class="Symbol">→</a> <a id="872" href="Algebra.Morphism.Definitions.html#418" class="Bound">B</a><a id="873" class="Symbol">)</a> <a id="875" class="Symbol">→</a> <a id="877" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="881" href="Algebra.Morphism.Definitions.html#366" class="Bound">A</a> <a id="883" class="Symbol">→</a> <a id="885" href="Algebra.Core.html#527" class="Function">Op₂</a> <a id="889" href="Algebra.Morphism.Definitions.html#418" class="Bound">B</a> <a id="891" class="Symbol">→</a> <a id="893" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="897" class="Symbol">_</a>
<a id="899" href="Algebra.Morphism.Definitions.html#852" class="Function">Homomorphic₂</a> <a id="912" href="Algebra.Morphism.Definitions.html#912" class="Bound Operator">⟦_⟧</a> <a id="916" href="Algebra.Morphism.Definitions.html#916" class="Bound Operator">_∙_</a> <a id="920" href="Algebra.Morphism.Definitions.html#920" class="Bound Operator">_∘_</a> <a id="924" class="Symbol">=</a> <a id="926" class="Symbol">∀</a> <a id="928" href="Algebra.Morphism.Definitions.html#928" class="Bound">x</a> <a id="930" href="Algebra.Morphism.Definitions.html#930" class="Bound">y</a> <a id="932" class="Symbol">→</a> <a id="934" href="Algebra.Morphism.Definitions.html#912" class="Bound Operator">⟦</a> <a id="936" href="Algebra.Morphism.Definitions.html#928" class="Bound">x</a> <a id="938" href="Algebra.Morphism.Definitions.html#916" class="Bound Operator">∙</a> <a id="940" href="Algebra.Morphism.Definitions.html#930" class="Bound">y</a> <a id="942" href="Algebra.Morphism.Definitions.html#912" class="Bound Operator">⟧</a> <a id="944" href="Algebra.Morphism.Definitions.html#472" class="Bound Operator">≈</a> <a id="946" class="Symbol">(</a><a id="947" href="Algebra.Morphism.Definitions.html#912" class="Bound Operator">⟦</a> <a id="949" href="Algebra.Morphism.Definitions.html#928" class="Bound">x</a> <a id="951" href="Algebra.Morphism.Definitions.html#912" class="Bound Operator">⟧</a> <a id="953" href="Algebra.Morphism.Definitions.html#920" class="Bound Operator">∘</a> <a id="955" href="Algebra.Morphism.Definitions.html#912" class="Bound Operator">⟦</a> <a id="957" href="Algebra.Morphism.Definitions.html#930" class="Bound">y</a> <a id="959" href="Algebra.Morphism.Definitions.html#912" class="Bound Operator">⟧</a><a id="960" class="Symbol">)</a>
<a id="963" class="Comment">------------------------------------------------------------------------</a>
<a id="1036" class="Comment">-- DEPRECATED NAMES</a>
<a id="1056" class="Comment">------------------------------------------------------------------------</a>
<a id="1129" class="Comment">-- Please use the new names as continuing support for the old names is</a>
<a id="1200" class="Comment">-- not guaranteed.</a>
<a id="1220" class="Comment">-- Version 1.3</a>
<a id="Morphism"></a><a id="1236" href="Algebra.Morphism.Definitions.html#1236" class="Function">Morphism</a> <a id="1245" class="Symbol">:</a> <a id="1247" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1251" class="Symbol">_</a>
<a id="1253" href="Algebra.Morphism.Definitions.html#1236" class="Function">Morphism</a> <a id="1262" class="Symbol">=</a> <a id="1264" href="Algebra.Morphism.Definitions.html#366" class="Bound">A</a> <a id="1266" class="Symbol">→</a> <a id="1268" href="Algebra.Morphism.Definitions.html#418" class="Bound">B</a>
<a id="1271" class="Symbol">{-#</a> <a id="1275" class="Keyword">WARNING_ON_USAGE</a> <a id="1292" class="Pragma">Morphism</a>
<a id="1301" class="String">&quot;Warning: Morphism was deprecated in v1.3.
Please use the standard function notation (e.g. A → B) instead.&quot;</a>
<a id="1409" class="Symbol">#-}</a>
</pre></body></html>
Reference in a new issue View git blame Copy permalink