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37 lines
12 KiB
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<html><head><meta charset="utf-8"><title>Categories.Diagram.Cocone</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="36" class="Keyword">open</a> <a id="41" class="Keyword">import</a> <a id="48" href="Categories.Category.html" class="Module">Categories.Category</a>
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<a id="68" class="Keyword">open</a> <a id="73" class="Keyword">import</a> <a id="80" href="Categories.Functor.html" class="Module">Categories.Functor</a> <a id="99" class="Keyword">hiding</a> <a id="106" class="Symbol">(</a><a id="107" href="Categories.Functor.html#349" class="Function">id</a><a id="109" class="Symbol">)</a>
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<a id="112" class="Comment">-- Cocone over a Functor F (from shape category J into category C)</a>
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<a id="180" class="Keyword">module</a> <a id="187" href="Categories.Diagram.Cocone.html" class="Module">Categories.Diagram.Cocone</a>
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<a id="215" class="Symbol">{</a><a id="216" href="Categories.Diagram.Cocone.html#216" class="Bound">o</a> <a id="218" href="Categories.Diagram.Cocone.html#218" class="Bound">ℓ</a> <a id="220" href="Categories.Diagram.Cocone.html#220" class="Bound">e</a><a id="221" class="Symbol">}</a> <a id="223" class="Symbol">{</a><a id="224" href="Categories.Diagram.Cocone.html#224" class="Bound">o′</a> <a id="227" href="Categories.Diagram.Cocone.html#227" class="Bound">ℓ′</a> <a id="230" href="Categories.Diagram.Cocone.html#230" class="Bound">e′</a><a id="232" class="Symbol">}</a> <a id="234" class="Symbol">{</a><a id="235" href="Categories.Diagram.Cocone.html#235" class="Bound">C</a> <a id="237" class="Symbol">:</a> <a id="239" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="248" href="Categories.Diagram.Cocone.html#216" class="Bound">o</a> <a id="250" href="Categories.Diagram.Cocone.html#218" class="Bound">ℓ</a> <a id="252" href="Categories.Diagram.Cocone.html#220" class="Bound">e</a><a id="253" class="Symbol">}</a> <a id="255" class="Symbol">{</a><a id="256" href="Categories.Diagram.Cocone.html#256" class="Bound">J</a> <a id="258" class="Symbol">:</a> <a id="260" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="269" href="Categories.Diagram.Cocone.html#224" class="Bound">o′</a> <a id="272" href="Categories.Diagram.Cocone.html#227" class="Bound">ℓ′</a> <a id="275" href="Categories.Diagram.Cocone.html#230" class="Bound">e′</a><a id="277" class="Symbol">}</a> <a id="279" class="Symbol">(</a><a id="280" href="Categories.Diagram.Cocone.html#280" class="Bound">F</a> <a id="282" class="Symbol">:</a> <a id="284" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="292" href="Categories.Diagram.Cocone.html#256" class="Bound">J</a> <a id="294" href="Categories.Diagram.Cocone.html#235" class="Bound">C</a><a id="295" class="Symbol">)</a> <a id="297" class="Keyword">where</a>
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<a id="304" class="Keyword">open</a> <a id="309" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="318" href="Categories.Diagram.Cocone.html#235" class="Bound">C</a>
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<a id="320" class="Keyword">open</a> <a id="325" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="333" href="Categories.Diagram.Cocone.html#280" class="Bound">F</a>
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<a id="336" class="Keyword">open</a> <a id="341" class="Keyword">import</a> <a id="348" href="Level.html" class="Module">Level</a>
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<a id="355" class="Keyword">record</a> <a id="Coapex"></a><a id="362" href="Categories.Diagram.Cocone.html#362" class="Record">Coapex</a> <a id="369" class="Symbol">(</a><a id="370" href="Categories.Diagram.Cocone.html#370" class="Bound">N</a> <a id="372" class="Symbol">:</a> <a id="374" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="377" class="Symbol">)</a> <a id="379" class="Symbol">:</a> <a id="381" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="385" class="Symbol">(</a><a id="386" href="Categories.Diagram.Cocone.html#216" class="Bound">o</a> <a id="388" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="390" href="Categories.Diagram.Cocone.html#218" class="Bound">ℓ</a> <a id="392" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="394" href="Categories.Diagram.Cocone.html#220" class="Bound">e</a> <a id="396" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="398" href="Categories.Diagram.Cocone.html#224" class="Bound">o′</a> <a id="401" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="403" href="Categories.Diagram.Cocone.html#227" class="Bound">ℓ′</a><a id="405" class="Symbol">)</a> <a id="407" class="Keyword">where</a>
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<a id="415" class="Keyword">field</a>
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<a id="Coapex.ψ"></a><a id="425" href="Categories.Diagram.Cocone.html#425" class="Field">ψ</a> <a id="433" class="Symbol">:</a> <a id="435" class="Symbol">(</a><a id="436" href="Categories.Diagram.Cocone.html#436" class="Bound">X</a> <a id="438" class="Symbol">:</a> <a id="440" href="Categories.Category.Core.html#559" class="Field">Category.Obj</a> <a id="453" href="Categories.Diagram.Cocone.html#256" class="Bound">J</a><a id="454" class="Symbol">)</a> <a id="456" class="Symbol">→</a> <a id="458" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="461" href="Categories.Diagram.Cocone.html#436" class="Bound">X</a> <a id="463" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="465" href="Categories.Diagram.Cocone.html#370" class="Bound">N</a>
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<a id="Coapex.commute"></a><a id="471" href="Categories.Diagram.Cocone.html#471" class="Field">commute</a> <a id="479" class="Symbol">:</a> <a id="481" class="Symbol">∀</a> <a id="483" class="Symbol">{</a><a id="484" href="Categories.Diagram.Cocone.html#484" class="Bound">X</a> <a id="486" href="Categories.Diagram.Cocone.html#486" class="Bound">Y</a><a id="487" class="Symbol">}</a> <a id="489" class="Symbol">(</a><a id="490" href="Categories.Diagram.Cocone.html#490" class="Bound">f</a> <a id="492" class="Symbol">:</a> <a id="494" href="Categories.Diagram.Cocone.html#256" class="Bound">J</a> <a id="496" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="498" href="Categories.Diagram.Cocone.html#484" class="Bound">X</a> <a id="500" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="502" href="Categories.Diagram.Cocone.html#486" class="Bound">Y</a> <a id="504" href="Categories.Category.html#502" class="Function Operator">]</a><a id="505" class="Symbol">)</a> <a id="507" class="Symbol">→</a> <a id="509" href="Categories.Diagram.Cocone.html#425" class="Field">ψ</a> <a id="511" href="Categories.Diagram.Cocone.html#486" class="Bound">Y</a> <a id="513" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="515" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="518" href="Categories.Diagram.Cocone.html#490" class="Bound">f</a> <a id="520" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="522" href="Categories.Diagram.Cocone.html#425" class="Field">ψ</a> <a id="524" href="Categories.Diagram.Cocone.html#484" class="Bound">X</a>
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<a id="527" class="Keyword">record</a> <a id="Cocone"></a><a id="534" href="Categories.Diagram.Cocone.html#534" class="Record">Cocone</a> <a id="541" class="Symbol">:</a> <a id="543" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="547" class="Symbol">(</a><a id="548" href="Categories.Diagram.Cocone.html#216" class="Bound">o</a> <a id="550" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="552" href="Categories.Diagram.Cocone.html#218" class="Bound">ℓ</a> <a id="554" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="556" href="Categories.Diagram.Cocone.html#220" class="Bound">e</a> <a id="558" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="560" href="Categories.Diagram.Cocone.html#224" class="Bound">o′</a> <a id="563" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="565" href="Categories.Diagram.Cocone.html#227" class="Bound">ℓ′</a><a id="567" 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="587" class="Symbol">{</a><a id="Cocone.N"></a><a id="588" href="Categories.Diagram.Cocone.html#588" class="Field">N</a><a id="589" class="Symbol">}</a> <a id="594" class="Symbol">:</a> <a id="596" href="Categories.Category.Core.html#559" class="Function">Obj</a>
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<a id="Cocone.coapex"></a><a id="604" href="Categories.Diagram.Cocone.html#604" class="Field">coapex</a> <a id="611" class="Symbol">:</a> <a id="613" href="Categories.Diagram.Cocone.html#362" class="Record">Coapex</a> <a id="620" href="Categories.Diagram.Cocone.html#588" class="Field">N</a>
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<a id="625" class="Keyword">open</a> <a id="630" href="Categories.Diagram.Cocone.html#362" class="Module">Coapex</a> <a id="637" href="Categories.Diagram.Cocone.html#604" class="Field">coapex</a> <a id="644" class="Keyword">public</a>
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<a id="652" class="Keyword">open</a> <a id="657" href="Categories.Diagram.Cocone.html#362" class="Module">Coapex</a>
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<a id="664" class="Keyword">open</a> <a id="669" href="Categories.Diagram.Cocone.html#534" class="Module">Cocone</a>
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<a id="677" class="Keyword">record</a> <a id="Cocone⇒"></a><a id="684" href="Categories.Diagram.Cocone.html#684" class="Record">Cocone⇒</a> <a id="692" class="Symbol">(</a><a id="693" href="Categories.Diagram.Cocone.html#693" class="Bound">c</a> <a id="695" href="Categories.Diagram.Cocone.html#695" class="Bound">c′</a> <a id="698" class="Symbol">:</a> <a id="700" href="Categories.Diagram.Cocone.html#534" class="Record">Cocone</a><a id="706" class="Symbol">)</a> <a id="708" class="Symbol">:</a> <a id="710" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="714" class="Symbol">(</a><a id="715" href="Categories.Diagram.Cocone.html#218" class="Bound">ℓ</a> <a id="717" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="719" href="Categories.Diagram.Cocone.html#220" class="Bound">e</a> <a id="721" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="723" href="Categories.Diagram.Cocone.html#224" class="Bound">o′</a><a id="725" class="Symbol">)</a> <a id="727" class="Keyword">where</a>
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<a id="735" class="Keyword">field</a>
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<a id="Cocone⇒.arr"></a><a id="745" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="753" class="Symbol">:</a> <a id="755" href="Categories.Diagram.Cocone.html#588" class="Field">N</a> <a id="757" href="Categories.Diagram.Cocone.html#693" class="Bound">c</a> <a id="759" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="761" href="Categories.Diagram.Cocone.html#588" class="Field">N</a> <a id="763" href="Categories.Diagram.Cocone.html#695" class="Bound">c′</a>
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<a id="Cocone⇒.commute"></a><a id="770" href="Categories.Diagram.Cocone.html#770" class="Field">commute</a> <a id="778" class="Symbol">:</a> <a id="780" class="Symbol">∀</a> <a id="782" class="Symbol">{</a><a id="783" href="Categories.Diagram.Cocone.html#783" class="Bound">X</a><a id="784" class="Symbol">}</a> <a id="786" class="Symbol">→</a> <a id="788" href="Categories.Diagram.Cocone.html#745" class="Field">arr</a> <a id="792" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="794" href="Categories.Diagram.Cocone.html#425" class="Field">ψ</a> <a id="796" href="Categories.Diagram.Cocone.html#693" class="Bound">c</a> <a id="798" href="Categories.Diagram.Cocone.html#783" class="Bound">X</a> <a id="800" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="802" href="Categories.Diagram.Cocone.html#425" class="Field">ψ</a> <a id="804" href="Categories.Diagram.Cocone.html#695" class="Bound">c′</a> <a id="807" href="Categories.Diagram.Cocone.html#783" class="Bound">X</a>
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<a id="810" class="Keyword">open</a> <a id="815" href="Categories.Diagram.Cocone.html#684" class="Module">Cocone⇒</a>
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</pre></body></html>
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