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33 lines
8.8 KiB
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<html><head><meta charset="utf-8"><title>Categories.Category.Extensive.Bundle</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>
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<a id="37" class="Comment">-- Bundled version of an extensive (distributive) Category</a>
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<a id="96" class="Keyword">module</a> <a id="103" href="Categories.Category.Extensive.Bundle.html" class="Module">Categories.Category.Extensive.Bundle</a> <a id="140" class="Keyword">where</a>
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<a id="147" class="Keyword">open</a> <a id="152" class="Keyword">import</a> <a id="159" href="Level.html" class="Module">Level</a>
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<a id="166" class="Keyword">open</a> <a id="171" class="Keyword">import</a> <a id="178" href="Categories.Category.Core.html" class="Module">Categories.Category.Core</a> <a id="203" class="Keyword">using</a> <a id="209" class="Symbol">(</a><a id="210" href="Categories.Category.Core.html#442" class="Record">Category</a><a id="218" class="Symbol">)</a>
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<a id="220" class="Keyword">open</a> <a id="225" class="Keyword">import</a> <a id="232" href="Categories.Category.Extensive.html" class="Module">Categories.Category.Extensive</a> <a id="262" class="Keyword">using</a> <a id="268" class="Symbol">(</a><a id="269" href="Categories.Category.Extensive.html#599" class="Record">Extensive</a><a id="278" class="Symbol">)</a>
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<a id="280" class="Keyword">open</a> <a id="285" class="Keyword">import</a> <a id="292" href="Categories.Category.Distributive.html" class="Module">Categories.Category.Distributive</a> <a id="325" class="Keyword">using</a> <a id="331" class="Symbol">(</a><a id="332" href="Categories.Category.Distributive.html#686" class="Record">Distributive</a><a id="344" class="Symbol">)</a>
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<a id="346" class="Keyword">open</a> <a id="351" class="Keyword">import</a> <a id="358" href="Categories.Category.Cartesian.html" class="Module">Categories.Category.Cartesian</a> <a id="388" class="Keyword">using</a> <a id="394" class="Symbol">(</a><a id="395" href="Categories.Category.Cartesian.html#727" class="Record">Cartesian</a><a id="404" class="Symbol">)</a>
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<a id="406" class="Keyword">open</a> <a id="411" class="Keyword">import</a> <a id="418" href="Categories.Category.Extensive.Properties.Distributive.html" class="Module">Categories.Category.Extensive.Properties.Distributive</a> <a id="472" class="Keyword">using</a> <a id="478" class="Symbol">(</a><a id="479" href="Categories.Category.Extensive.Properties.Distributive.html#1506" class="Function">Extensive×Cartesian⇒Distributive</a><a id="511" class="Symbol">)</a>
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<a id="514" class="Keyword">record</a> <a id="ExtensiveCategory"></a><a id="521" href="Categories.Category.Extensive.Bundle.html#521" class="Record">ExtensiveCategory</a> <a id="539" href="Categories.Category.Extensive.Bundle.html#539" class="Bound">o</a> <a id="541" href="Categories.Category.Extensive.Bundle.html#541" class="Bound">ℓ</a> <a id="543" href="Categories.Category.Extensive.Bundle.html#543" class="Bound">e</a> <a id="545" class="Symbol">:</a> <a id="547" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="551" class="Symbol">(</a><a id="552" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="556" class="Symbol">(</a><a id="557" href="Categories.Category.Extensive.Bundle.html#539" class="Bound">o</a> <a id="559" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="561" href="Categories.Category.Extensive.Bundle.html#541" class="Bound">ℓ</a> <a id="563" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="565" href="Categories.Category.Extensive.Bundle.html#543" class="Bound">e</a><a id="566" class="Symbol">))</a> <a id="569" class="Keyword">where</a>
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<a id="577" class="Keyword">field</a>
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<a id="ExtensiveCategory.U"></a><a id="587" href="Categories.Category.Extensive.Bundle.html#587" class="Field">U</a> <a id="599" class="Symbol">:</a> <a id="601" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="610" href="Categories.Category.Extensive.Bundle.html#539" class="Bound">o</a> <a id="612" href="Categories.Category.Extensive.Bundle.html#541" class="Bound">ℓ</a> <a id="614" href="Categories.Category.Extensive.Bundle.html#543" class="Bound">e</a> <a id="617" class="Comment">-- U for underlying</a>
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<a id="ExtensiveCategory.extensive"></a><a id="641" href="Categories.Category.Extensive.Bundle.html#641" class="Field">extensive</a> <a id="653" class="Symbol">:</a> <a id="655" href="Categories.Category.Extensive.html#599" class="Record">Extensive</a> <a id="665" href="Categories.Category.Extensive.Bundle.html#587" class="Field">U</a>
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<a id="670" class="Keyword">open</a> <a id="675" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="684" href="Categories.Category.Extensive.Bundle.html#587" class="Field">U</a> <a id="686" class="Keyword">public</a>
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<a id="695" class="Keyword">open</a> <a id="700" href="Categories.Category.Extensive.html#599" class="Module">Extensive</a> <a id="710" href="Categories.Category.Extensive.Bundle.html#641" class="Field">extensive</a> <a id="720" class="Keyword">public</a>
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<a id="728" class="Comment">-- An extensive category with finite products</a>
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<a id="774" class="Keyword">record</a> <a id="ExtensiveDistributiveCategory"></a><a id="781" href="Categories.Category.Extensive.Bundle.html#781" class="Record">ExtensiveDistributiveCategory</a> <a id="811" href="Categories.Category.Extensive.Bundle.html#811" class="Bound">o</a> <a id="813" href="Categories.Category.Extensive.Bundle.html#813" class="Bound">ℓ</a> <a id="815" href="Categories.Category.Extensive.Bundle.html#815" class="Bound">e</a> <a id="817" class="Symbol">:</a> <a id="819" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="823" class="Symbol">(</a><a id="824" href="Agda.Primitive.html#774" class="Primitive">suc</a> <a id="828" class="Symbol">(</a><a id="829" href="Categories.Category.Extensive.Bundle.html#811" class="Bound">o</a> <a id="831" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="833" href="Categories.Category.Extensive.Bundle.html#813" class="Bound">ℓ</a> <a id="835" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="837" href="Categories.Category.Extensive.Bundle.html#815" class="Bound">e</a><a id="838" class="Symbol">))</a> <a id="841" class="Keyword">where</a>
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<a id="849" class="Keyword">field</a>
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<a id="ExtensiveDistributiveCategory.U"></a><a id="859" href="Categories.Category.Extensive.Bundle.html#859" class="Field">U</a> <a id="871" class="Symbol">:</a> <a id="873" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="882" href="Categories.Category.Extensive.Bundle.html#811" class="Bound">o</a> <a id="884" href="Categories.Category.Extensive.Bundle.html#813" class="Bound">ℓ</a> <a id="886" href="Categories.Category.Extensive.Bundle.html#815" class="Bound">e</a> <a id="889" class="Comment">-- U for underlying</a>
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<a id="ExtensiveDistributiveCategory.extensive"></a><a id="913" href="Categories.Category.Extensive.Bundle.html#913" class="Field">extensive</a> <a id="925" class="Symbol">:</a> <a id="927" href="Categories.Category.Extensive.html#599" class="Record">Extensive</a> <a id="937" href="Categories.Category.Extensive.Bundle.html#859" class="Field">U</a>
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<a id="ExtensiveDistributiveCategory.cartesian"></a><a id="943" href="Categories.Category.Extensive.Bundle.html#943" class="Field">cartesian</a> <a id="955" class="Symbol">:</a> <a id="957" href="Categories.Category.Cartesian.html#727" class="Record">Cartesian</a> <a id="967" href="Categories.Category.Extensive.Bundle.html#859" class="Field">U</a>
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<a id="972" class="Keyword">open</a> <a id="977" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="986" href="Categories.Category.Extensive.Bundle.html#859" class="Field">U</a> <a id="988" class="Keyword">public</a>
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<a id="997" class="Keyword">open</a> <a id="1002" href="Categories.Category.Extensive.html#599" class="Module">Extensive</a> <a id="1012" href="Categories.Category.Extensive.Bundle.html#913" class="Field">extensive</a> <a id="1022" class="Keyword">public</a>
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<a id="1031" class="Keyword">open</a> <a id="1036" href="Categories.Category.Distributive.html#686" class="Module">Distributive</a> <a id="1049" class="Symbol">(</a><a id="1050" href="Categories.Category.Extensive.Properties.Distributive.html#1506" class="Function">Extensive×Cartesian⇒Distributive</a> <a id="1083" href="Categories.Category.Extensive.Bundle.html#859" class="Field">U</a> <a id="1085" href="Categories.Category.Extensive.Bundle.html#913" class="Field">extensive</a> <a id="1095" href="Categories.Category.Extensive.Bundle.html#943" class="Field">cartesian</a><a id="1104" class="Symbol">)</a> <a id="1106" class="Keyword">public</a>
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</pre></body></html>
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