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bsc-leon-vatthauer/agda/bsc-thesis/Categories.Functor.Construction.Constant.html
Leon Vatthauer 2bf4655eae
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<html><head><meta charset="utf-8"><title>Categories.Functor.Construction.Constant</title><link rel="stylesheet" href="Agda.css"></head><body><pre class="Agda"><a id="1" class="Symbol">{-#</a> <a id="5" class="Keyword">OPTIONS</a> <a id="13" class="Pragma">--without-K</a> <a id="25" class="Pragma">--safe</a> <a id="32" class="Symbol">#-}</a>
<a id="36" class="Keyword">module</a> <a id="43" href="Categories.Functor.Construction.Constant.html" class="Module">Categories.Functor.Construction.Constant</a> <a id="84" class="Keyword">where</a>
<a id="91" class="Keyword">open</a> <a id="96" class="Keyword">import</a> <a id="103" href="Level.html" class="Module">Level</a>
<a id="110" class="Keyword">open</a> <a id="115" class="Keyword">import</a> <a id="122" href="Categories.Category.html" class="Module">Categories.Category</a>
<a id="142" class="Keyword">open</a> <a id="147" class="Keyword">import</a> <a id="154" href="Categories.Category.Instance.One.html" class="Module">Categories.Category.Instance.One</a>
<a id="187" class="Keyword">open</a> <a id="192" class="Keyword">import</a> <a id="199" href="Categories.Category.Product.html" class="Module">Categories.Category.Product</a>
<a id="227" class="Keyword">open</a> <a id="232" class="Keyword">import</a> <a id="239" href="Categories.Functor.html" class="Module">Categories.Functor</a> <a id="258" class="Keyword">renaming</a> <a id="267" class="Symbol">(</a><a id="268" href="Categories.Functor.html#349" class="Function">id</a> <a id="271" class="Symbol">to</a> <a id="274" class="Function">idF</a><a id="277" class="Symbol">)</a>
<a id="279" class="Keyword">open</a> <a id="284" class="Keyword">import</a> <a id="291" href="Categories.NaturalTransformation.html" class="Module">Categories.NaturalTransformation</a> <a id="324" class="Keyword">using</a> <a id="330" class="Symbol">(</a><a id="331" href="Categories.NaturalTransformation.Core.html#466" class="Record">NaturalTransformation</a><a id="352" class="Symbol">)</a>
<a id="354" class="Keyword">import</a> <a id="361" href="Categories.Morphism.Reasoning.html" class="Module">Categories.Morphism.Reasoning</a> <a id="391" class="Symbol">as</a> <a id="394" class="Module">MR</a>
<a id="398" class="Keyword">private</a>
<a id="408" class="Keyword">variable</a>
<a id="421" href="Categories.Functor.Construction.Constant.html#421" class="Generalizable">o</a> <a id="423" href="Categories.Functor.Construction.Constant.html#423" class="Generalizable">ℓ</a> <a id="425" href="Categories.Functor.Construction.Constant.html#425" class="Generalizable">e</a> <a id="427" class="Symbol">:</a> <a id="429" href="Agda.Primitive.html#742" class="Postulate">Level</a>
<a id="439" href="Categories.Functor.Construction.Constant.html#439" class="Generalizable">C</a> <a id="441" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a> <a id="443" class="Symbol">:</a> <a id="445" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="454" href="Categories.Functor.Construction.Constant.html#421" class="Generalizable">o</a> <a id="456" href="Categories.Functor.Construction.Constant.html#423" class="Generalizable">ℓ</a> <a id="458" href="Categories.Functor.Construction.Constant.html#425" class="Generalizable">e</a>
<a id="const"></a><a id="461" href="Categories.Functor.Construction.Constant.html#461" class="Function">const</a> <a id="467" class="Symbol">:</a> <a id="469" class="Symbol">(</a><a id="470" href="Categories.Functor.Construction.Constant.html#470" class="Bound">d</a> <a id="472" class="Symbol">:</a> <a id="474" href="Categories.Category.Core.html#559" class="Field">Category.Obj</a> <a id="487" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a><a id="488" class="Symbol">)</a> <a id="490" class="Symbol">→</a> <a id="492" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="500" href="Categories.Functor.Construction.Constant.html#439" class="Generalizable">C</a> <a id="502" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a>
<a id="504" href="Categories.Functor.Construction.Constant.html#461" class="Function">const</a> <a id="510" class="Symbol">{</a><a id="511" class="Argument">D</a> <a id="513" class="Symbol">=</a> <a id="515" href="Categories.Functor.Construction.Constant.html#515" class="Bound">D</a><a id="516" class="Symbol">}</a> <a id="518" href="Categories.Functor.Construction.Constant.html#518" class="Bound">d</a> <a id="520" class="Symbol">=</a> <a id="522" class="Keyword">record</a>
<a id="531" class="Symbol">{</a> <a id="533" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="546" class="Symbol">=</a> <a id="548" class="Symbol">λ</a> <a id="550" href="Categories.Functor.Construction.Constant.html#550" class="Bound">_</a> <a id="552" class="Symbol">→</a> <a id="554" href="Categories.Functor.Construction.Constant.html#518" class="Bound">d</a>
<a id="558" class="Symbol">;</a> <a id="560" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="573" class="Symbol">=</a> <a id="575" class="Symbol">λ</a> <a id="577" href="Categories.Functor.Construction.Constant.html#577" class="Bound">_</a> <a id="579" class="Symbol">→</a> <a id="581" href="Categories.Category.Core.html#630" class="Function">id</a>
<a id="586" class="Symbol">;</a> <a id="588" href="Categories.Functor.Core.html#511" class="Field">identity</a> <a id="601" class="Symbol">=</a> <a id="603" href="Relation.Binary.Structures.html#1596" class="Function">refl</a>
<a id="610" class="Symbol">;</a> <a id="612" href="Categories.Functor.Core.html#565" class="Field">homomorphism</a> <a id="625" class="Symbol">=</a> <a id="627" href="Relation.Binary.Structures.html#1622" class="Function">sym</a> <a id="631" href="Categories.Category.Core.html#1339" class="Function">identity²</a>
<a id="643" class="Symbol">;</a> <a id="645" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a> <a id="658" class="Symbol">=</a> <a id="660" class="Symbol">λ</a> <a id="662" href="Categories.Functor.Construction.Constant.html#662" class="Bound">_</a> <a id="664" class="Symbol">→</a> <a id="666" href="Relation.Binary.Structures.html#1596" class="Function">refl</a>
<a id="673" class="Symbol">}</a>
<a id="677" class="Keyword">where</a> <a id="683" class="Keyword">open</a> <a id="688" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="697" href="Categories.Functor.Construction.Constant.html#515" class="Bound">D</a>
<a id="707" class="Keyword">open</a> <a id="712" href="Categories.Category.Core.html#1530" class="Module">Equiv</a>
<a id="const!"></a><a id="719" href="Categories.Functor.Construction.Constant.html#719" class="Function">const!</a> <a id="726" class="Symbol">:</a> <a id="728" class="Symbol">(</a><a id="729" href="Categories.Functor.Construction.Constant.html#729" class="Bound">d</a> <a id="731" class="Symbol">:</a> <a id="733" href="Categories.Category.Core.html#559" class="Field">Category.Obj</a> <a id="746" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a><a id="747" class="Symbol">)</a> <a id="749" class="Symbol">→</a> <a id="751" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="759" class="Symbol">(</a><a id="760" href="Categories.Category.Instance.One.html#351" class="Function">One</a> <a id="764" class="Symbol">{</a><a id="765" href="Level.html#521" class="Function">0ℓ</a><a id="767" class="Symbol">}</a> <a id="769" class="Symbol">{</a><a id="770" href="Level.html#521" class="Function">0ℓ</a><a id="772" class="Symbol">}</a> <a id="774" class="Symbol">{</a><a id="775" href="Level.html#521" class="Function">0ℓ</a><a id="777" class="Symbol">})</a> <a id="780" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a>
<a id="782" href="Categories.Functor.Construction.Constant.html#719" class="Function">const!</a> <a id="789" class="Symbol">=</a> <a id="791" href="Categories.Functor.Construction.Constant.html#461" class="Function">const</a>
<a id="constˡ"></a><a id="798" href="Categories.Functor.Construction.Constant.html#798" class="Function">constˡ</a> <a id="805" class="Symbol">:</a> <a id="807" class="Symbol">(</a><a id="808" href="Categories.Functor.Construction.Constant.html#808" class="Bound">c</a> <a id="810" class="Symbol">:</a> <a id="812" href="Categories.Category.Core.html#559" class="Field">Category.Obj</a> <a id="825" href="Categories.Functor.Construction.Constant.html#439" class="Generalizable">C</a><a id="826" class="Symbol">)</a> <a id="828" class="Symbol">→</a> <a id="830" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="838" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a> <a id="840" class="Symbol">(</a><a id="841" href="Categories.Category.Product.html#745" class="Function">Product</a> <a id="849" href="Categories.Functor.Construction.Constant.html#439" class="Generalizable">C</a> <a id="851" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a><a id="852" class="Symbol">)</a>
<a id="854" href="Categories.Functor.Construction.Constant.html#798" class="Function">constˡ</a> <a id="861" href="Categories.Functor.Construction.Constant.html#861" class="Bound">c</a> <a id="863" class="Symbol">=</a> <a id="865" href="Categories.Functor.Construction.Constant.html#461" class="Function">const</a> <a id="871" href="Categories.Functor.Construction.Constant.html#861" class="Bound">c</a> <a id="873" href="Categories.Category.Product.html#1553" class="Function Operator">※</a> <a id="875" href="Categories.Functor.Construction.Constant.html#274" class="Function">idF</a>
<a id="constʳ"></a><a id="880" href="Categories.Functor.Construction.Constant.html#880" class="Function">constʳ</a> <a id="887" class="Symbol">:</a> <a id="889" class="Symbol">(</a><a id="890" href="Categories.Functor.Construction.Constant.html#890" class="Bound">c</a> <a id="892" class="Symbol">:</a> <a id="894" href="Categories.Category.Core.html#559" class="Field">Category.Obj</a> <a id="907" href="Categories.Functor.Construction.Constant.html#439" class="Generalizable">C</a><a id="908" class="Symbol">)</a> <a id="910" class="Symbol">→</a> <a id="912" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="920" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a> <a id="922" class="Symbol">(</a><a id="923" href="Categories.Category.Product.html#745" class="Function">Product</a> <a id="931" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a> <a id="933" href="Categories.Functor.Construction.Constant.html#439" class="Generalizable">C</a><a id="934" class="Symbol">)</a>
<a id="936" href="Categories.Functor.Construction.Constant.html#880" class="Function">constʳ</a> <a id="943" href="Categories.Functor.Construction.Constant.html#943" class="Bound">c</a> <a id="945" class="Symbol">=</a> <a id="947" href="Categories.Functor.Construction.Constant.html#274" class="Function">idF</a> <a id="951" href="Categories.Category.Product.html#1553" class="Function Operator">※</a> <a id="953" class="Symbol">(</a><a id="954" href="Categories.Functor.Construction.Constant.html#461" class="Function">const</a> <a id="960" href="Categories.Functor.Construction.Constant.html#943" class="Bound">c</a><a id="961" class="Symbol">)</a>
<a id="constNat"></a><a id="964" href="Categories.Functor.Construction.Constant.html#964" class="Function">constNat</a> <a id="973" class="Symbol">:</a> <a id="975" class="Symbol">∀</a> <a id="977" class="Symbol">{</a><a id="978" href="Categories.Functor.Construction.Constant.html#978" class="Bound">A</a> <a id="980" href="Categories.Functor.Construction.Constant.html#980" class="Bound">B</a><a id="981" class="Symbol">}</a> <a id="983" class="Symbol">→</a> <a id="985" href="Categories.Category.Core.html#575" class="Field Operator">Category._⇒_</a> <a id="998" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a> <a id="1000" href="Categories.Functor.Construction.Constant.html#978" class="Bound">A</a> <a id="1002" href="Categories.Functor.Construction.Constant.html#980" class="Bound">B</a> <a id="1004" class="Symbol">→</a> <a id="1006" href="Categories.NaturalTransformation.Core.html#466" class="Record">NaturalTransformation</a> <a id="1028" class="Symbol">(</a><a id="1029" href="Categories.Functor.Construction.Constant.html#461" class="Function">const</a> <a id="1035" class="Symbol">{</a><a id="1036" class="Argument">D</a> <a id="1038" class="Symbol">=</a> <a id="1040" href="Categories.Functor.Construction.Constant.html#441" class="Generalizable">D</a><a id="1041" class="Symbol">}</a> <a id="1043" class="Symbol">{</a><a id="1044" class="Argument">C</a> <a id="1046" class="Symbol">=</a> <a id="1048" href="Categories.Functor.Construction.Constant.html#439" class="Generalizable">C</a><a id="1049" class="Symbol">}</a> <a id="1051" href="Categories.Functor.Construction.Constant.html#978" class="Bound">A</a><a id="1052" class="Symbol">)</a> <a id="1054" class="Symbol">(</a><a id="1055" href="Categories.Functor.Construction.Constant.html#461" class="Function">const</a> <a id="1061" href="Categories.Functor.Construction.Constant.html#980" class="Bound">B</a><a id="1062" class="Symbol">)</a>
<a id="1064" href="Categories.Functor.Construction.Constant.html#964" class="Function">constNat</a> <a id="1073" class="Symbol">{</a><a id="1074" class="Argument">D</a> <a id="1076" class="Symbol">=</a> <a id="1078" href="Categories.Functor.Construction.Constant.html#1078" class="Bound">D</a><a id="1079" class="Symbol">}</a> <a id="1081" href="Categories.Functor.Construction.Constant.html#1081" class="Bound">f</a> <a id="1083" class="Symbol">=</a> <a id="1085" class="Keyword">record</a>
<a id="1094" class="Symbol">{</a> <a id="1096" href="Categories.NaturalTransformation.Core.html#783" class="Field">η</a> <a id="1108" class="Symbol">=</a> <a id="1110" class="Symbol">λ</a> <a id="1112" href="Categories.Functor.Construction.Constant.html#1112" class="Bound">_</a> <a id="1114" class="Symbol">→</a> <a id="1116" href="Categories.Functor.Construction.Constant.html#1081" class="Bound">f</a>
<a id="1120" class="Symbol">;</a> <a id="1122" href="Categories.NaturalTransformation.Core.html#827" class="Field">commute</a> <a id="1134" class="Symbol">=</a> <a id="1136" class="Symbol">λ</a> <a id="1138" href="Categories.Functor.Construction.Constant.html#1138" class="Bound">_</a> <a id="1140" class="Symbol">→</a> <a id="1142" href="Categories.Morphism.Reasoning.Core.html#1202" class="Function">MR.id-comm</a> <a id="1153" href="Categories.Functor.Construction.Constant.html#1078" class="Bound">D</a>
<a id="1157" class="Symbol">;</a> <a id="1159" href="Categories.NaturalTransformation.Core.html#1043" class="Field">sym-commute</a> <a id="1171" class="Symbol">=</a> <a id="1173" class="Symbol">λ</a> <a id="1175" href="Categories.Functor.Construction.Constant.html#1175" class="Bound">_</a> <a id="1177" class="Symbol">→</a> <a id="1179" href="Categories.Morphism.Reasoning.Core.html#1309" class="Function">MR.id-comm-sym</a> <a id="1194" href="Categories.Functor.Construction.Constant.html#1078" class="Bound">D</a>
<a id="1198" class="Symbol">}</a>
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