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| <!DOCTYPE HTML> | ||
| <html><head><meta charset="utf-8"><title>Cubical.Categories.Site.Cover</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">--safe</a> <a id="20" class="Symbol">#-}</a> | ||
| <a id="24" class="Keyword">module</a> <a id="31" href="Cubical.Categories.Site.Cover.html" class="Module">Cubical.Categories.Site.Cover</a> <a id="61" class="Keyword">where</a> | ||
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| <a id="68" class="Comment">-- A cover of an object is just a family of arrows into that object.</a> | ||
| <a id="137" class="Comment">-- This notion is used in the definition of a coverage.</a> | ||
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| <a id="194" class="Keyword">open</a> <a id="199" class="Keyword">import</a> <a id="206" href="Cubical.Foundations.Prelude.html" class="Module">Cubical.Foundations.Prelude</a> | ||
| <a id="234" class="Keyword">open</a> <a id="239" class="Keyword">import</a> <a id="246" href="Cubical.Foundations.Structure.html" class="Module">Cubical.Foundations.Structure</a> | ||
| <a id="276" class="Keyword">open</a> <a id="281" class="Keyword">import</a> <a id="288" href="Cubical.HITs.PropositionalTruncation.html" class="Module">Cubical.HITs.PropositionalTruncation</a> | ||
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| <a id="326" class="Keyword">open</a> <a id="331" class="Keyword">import</a> <a id="338" href="Cubical.Categories.Category.html" class="Module">Cubical.Categories.Category</a> | ||
| <a id="366" class="Keyword">open</a> <a id="371" class="Keyword">import</a> <a id="378" href="Cubical.Categories.Constructions.Slice.html" class="Module">Cubical.Categories.Constructions.Slice</a> | ||
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| <a id="419" class="Keyword">module</a> <a id="426" href="Cubical.Categories.Site.Cover.html#426" class="Module">_</a> | ||
| <a id="430" class="Symbol">{</a><a id="431" href="Cubical.Categories.Site.Cover.html#431" class="Bound">ℓ</a> <a id="433" href="Cubical.Categories.Site.Cover.html#433" class="Bound">ℓ'</a> <a id="436" class="Symbol">:</a> <a id="438" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="443" class="Symbol">}</a> | ||
| <a id="447" class="Symbol">(</a><a id="448" href="Cubical.Categories.Site.Cover.html#448" class="Bound">C</a> <a id="450" class="Symbol">:</a> <a id="452" href="Cubical.Categories.Category.Base.html#334" class="Record">Category</a> <a id="461" href="Cubical.Categories.Site.Cover.html#431" class="Bound">ℓ</a> <a id="463" href="Cubical.Categories.Site.Cover.html#433" class="Bound">ℓ'</a><a id="465" class="Symbol">)</a> | ||
| <a id="469" class="Keyword">where</a> | ||
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| <a id="478" class="Keyword">open</a> <a id="483" href="Cubical.Categories.Category.Base.html#334" class="Module">Category</a> | ||
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| <a id="495" href="Cubical.Categories.Site.Cover.html#495" class="Function">Cover</a> <a id="501" class="Symbol">:</a> <a id="503" class="Symbol">(</a><a id="504" href="Cubical.Categories.Site.Cover.html#504" class="Bound">ℓpat</a> <a id="509" class="Symbol">:</a> <a id="511" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="516" class="Symbol">)</a> <a id="518" class="Symbol">→</a> <a id="520" href="Cubical.Categories.Category.Base.html#452" class="Field">ob</a> <a id="523" href="Cubical.Categories.Site.Cover.html#448" class="Bound">C</a> <a id="525" class="Symbol">→</a> <a id="527" href="Agda.Primitive.html#388" class="Primitive">Type</a> <a id="532" class="Symbol">(</a><a id="533" href="Agda.Primitive.html#961" class="Primitive">ℓ-max</a> <a id="539" class="Symbol">(</a><a id="540" href="Agda.Primitive.html#961" class="Primitive">ℓ-max</a> <a id="546" href="Cubical.Categories.Site.Cover.html#431" class="Bound">ℓ</a> <a id="548" href="Cubical.Categories.Site.Cover.html#433" class="Bound">ℓ'</a><a id="550" class="Symbol">)</a> <a id="552" class="Symbol">(</a><a id="553" href="Agda.Primitive.html#931" class="Primitive">ℓ-suc</a> <a id="559" href="Cubical.Categories.Site.Cover.html#504" class="Bound">ℓpat</a><a id="563" class="Symbol">))</a> | ||
| <a id="568" href="Cubical.Categories.Site.Cover.html#495" class="Function">Cover</a> <a id="574" href="Cubical.Categories.Site.Cover.html#574" class="Bound">ℓpat</a> <a id="579" href="Cubical.Categories.Site.Cover.html#579" class="Bound">c</a> <a id="581" class="Symbol">=</a> <a id="583" href="Cubical.Foundations.Structure.html#399" class="Function">TypeWithStr</a> <a id="595" href="Cubical.Categories.Site.Cover.html#574" class="Bound">ℓpat</a> <a id="600" class="Symbol">λ</a> <a id="602" href="Cubical.Categories.Site.Cover.html#602" class="Bound">patches</a> <a id="610" class="Symbol">→</a> <a id="612" href="Cubical.Categories.Site.Cover.html#602" class="Bound">patches</a> <a id="620" class="Symbol">→</a> <a id="622" href="Cubical.Categories.Category.Base.html#452" class="Field">ob</a> <a id="625" class="Symbol">(</a><a id="626" href="Cubical.Categories.Constructions.Slice.Base.html#3368" class="Function">SliceCat</a> <a id="635" href="Cubical.Categories.Site.Cover.html#448" class="Bound">C</a> <a id="637" href="Cubical.Categories.Site.Cover.html#579" class="Bound">c</a><a id="638" class="Symbol">)</a> | ||
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| <a id="641" class="Keyword">module</a> <a id="648" href="Cubical.Categories.Site.Cover.html#648" class="Module">_</a> | ||
| <a id="652" class="Symbol">{</a><a id="653" href="Cubical.Categories.Site.Cover.html#653" class="Bound">ℓ</a> <a id="655" href="Cubical.Categories.Site.Cover.html#655" class="Bound">ℓ'</a> <a id="658" class="Symbol">:</a> <a id="660" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="665" class="Symbol">}</a> | ||
| <a id="669" class="Symbol">{</a><a id="670" href="Cubical.Categories.Site.Cover.html#670" class="Bound">C</a> <a id="672" class="Symbol">:</a> <a id="674" href="Cubical.Categories.Category.Base.html#334" class="Record">Category</a> <a id="683" href="Cubical.Categories.Site.Cover.html#653" class="Bound">ℓ</a> <a id="685" href="Cubical.Categories.Site.Cover.html#655" class="Bound">ℓ'</a><a id="687" class="Symbol">}</a> | ||
| <a id="691" class="Keyword">where</a> | ||
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| <a id="700" class="Keyword">open</a> <a id="705" href="Cubical.Categories.Category.Base.html#334" class="Module">Category</a> | ||
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| <a id="717" class="Comment">-- Extracting the members (patches) from a cover.</a> | ||
| <a id="769" class="Keyword">module</a> <a id="776" href="Cubical.Categories.Site.Cover.html#776" class="Module">_</a> | ||
| <a id="782" class="Symbol">{</a><a id="783" href="Cubical.Categories.Site.Cover.html#783" class="Bound">ℓpat</a> <a id="788" class="Symbol">:</a> <a id="790" href="Agda.Primitive.html#742" class="Postulate">Level</a><a id="795" class="Symbol">}</a> | ||
| <a id="801" class="Symbol">{</a><a id="802" href="Cubical.Categories.Site.Cover.html#802" class="Bound">c</a> <a id="804" class="Symbol">:</a> <a id="806" href="Cubical.Categories.Category.Base.html#452" class="Field">ob</a> <a id="809" href="Cubical.Categories.Site.Cover.html#670" class="Bound">C</a><a id="810" class="Symbol">}</a> | ||
| <a id="816" class="Symbol">(</a><a id="817" href="Cubical.Categories.Site.Cover.html#817" class="Bound">cov</a> <a id="821" class="Symbol">:</a> <a id="823" href="Cubical.Categories.Site.Cover.html#495" class="Function">Cover</a> <a id="829" href="Cubical.Categories.Site.Cover.html#670" class="Bound">C</a> <a id="831" href="Cubical.Categories.Site.Cover.html#783" class="Bound">ℓpat</a> <a id="836" href="Cubical.Categories.Site.Cover.html#802" class="Bound">c</a><a id="837" class="Symbol">)</a> | ||
| <a id="843" class="Symbol">(</a><a id="844" href="Cubical.Categories.Site.Cover.html#844" class="Bound">patch</a> <a id="850" class="Symbol">:</a> <a id="852" href="Cubical.Foundations.Structure.html#640" class="Function Operator">⟨</a> <a id="854" href="Cubical.Categories.Site.Cover.html#817" class="Bound">cov</a> <a id="858" href="Cubical.Foundations.Structure.html#640" class="Function Operator">⟩</a><a id="859" class="Symbol">)</a> | ||
| <a id="865" class="Keyword">where</a> | ||
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| <a id="876" href="Cubical.Categories.Site.Cover.html#876" class="Function">patchObj</a> <a id="885" class="Symbol">:</a> <a id="887" href="Cubical.Categories.Category.Base.html#452" class="Field">ob</a> <a id="890" href="Cubical.Categories.Site.Cover.html#670" class="Bound">C</a> | ||
| <a id="896" href="Cubical.Categories.Site.Cover.html#876" class="Function">patchObj</a> <a id="905" class="Symbol">=</a> <a id="907" href="Cubical.Categories.Constructions.Slice.Base.html#777" class="Field">S-ob</a> <a id="912" class="Symbol">(</a><a id="913" href="Cubical.Foundations.Structure.html#557" class="Function">str</a> <a id="917" href="Cubical.Categories.Site.Cover.html#817" class="Bound">cov</a> <a id="921" href="Cubical.Categories.Site.Cover.html#844" class="Bound">patch</a><a id="926" class="Symbol">)</a> | ||
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| <a id="933" href="Cubical.Categories.Site.Cover.html#933" class="Function">patchArr</a> <a id="942" class="Symbol">:</a> <a id="944" href="Cubical.Categories.Site.Cover.html#670" class="Bound">C</a> <a id="946" href="Cubical.Categories.Category.Base.html#1083" class="Function Operator">[</a> <a id="948" href="Cubical.Categories.Site.Cover.html#876" class="Function">patchObj</a> <a id="957" href="Cubical.Categories.Category.Base.html#1083" class="Function Operator">,</a> <a id="959" href="Cubical.Categories.Site.Cover.html#802" class="Bound">c</a> <a id="961" href="Cubical.Categories.Category.Base.html#1083" class="Function Operator">]</a> | ||
| <a id="967" href="Cubical.Categories.Site.Cover.html#933" class="Function">patchArr</a> <a id="976" class="Symbol">=</a> <a id="978" href="Cubical.Categories.Constructions.Slice.Base.html#795" class="Field">S-arr</a> <a id="984" class="Symbol">(</a><a id="985" href="Cubical.Foundations.Structure.html#557" class="Function">str</a> <a id="989" href="Cubical.Categories.Site.Cover.html#817" class="Bound">cov</a> <a id="993" href="Cubical.Categories.Site.Cover.html#844" class="Bound">patch</a><a id="998" class="Symbol">)</a> | ||
| </pre></body></html> |
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