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<html><head><meta charset="utf-8"><title>Categories.Diagram.Cone</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">open</a> <a id="41" class="Keyword">import</a> <a id="48" href="Categories.Category.html" class="Module">Categories.Category</a>
<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>
<a id="112" class="Comment">-- Cone over a Functor F (from shape category J into category C)</a>
<a id="178" class="Keyword">module</a> <a id="185" href="Categories.Diagram.Cone.html" class="Module">Categories.Diagram.Cone</a>
<a id="211" class="Symbol">{</a><a id="212" href="Categories.Diagram.Cone.html#212" class="Bound">o</a> <a id="214" href="Categories.Diagram.Cone.html#214" class="Bound">ℓ</a> <a id="216" href="Categories.Diagram.Cone.html#216" class="Bound">e</a><a id="217" class="Symbol">}</a> <a id="219" class="Symbol">{</a><a id="220" href="Categories.Diagram.Cone.html#220" class="Bound">o′</a> <a id="223" href="Categories.Diagram.Cone.html#223" class="Bound">ℓ′</a> <a id="226" href="Categories.Diagram.Cone.html#226" class="Bound">e′</a><a id="228" class="Symbol">}</a> <a id="230" class="Symbol">{</a><a id="231" href="Categories.Diagram.Cone.html#231" class="Bound">C</a> <a id="233" class="Symbol">:</a> <a id="235" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="244" href="Categories.Diagram.Cone.html#212" class="Bound">o</a> <a id="246" href="Categories.Diagram.Cone.html#214" class="Bound">ℓ</a> <a id="248" href="Categories.Diagram.Cone.html#216" class="Bound">e</a><a id="249" class="Symbol">}</a> <a id="251" class="Symbol">{</a><a id="252" href="Categories.Diagram.Cone.html#252" class="Bound">J</a> <a id="254" class="Symbol">:</a> <a id="256" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="265" href="Categories.Diagram.Cone.html#220" class="Bound">o′</a> <a id="268" href="Categories.Diagram.Cone.html#223" class="Bound">ℓ′</a> <a id="271" href="Categories.Diagram.Cone.html#226" class="Bound">e′</a><a id="273" class="Symbol">}</a> <a id="275" class="Symbol">(</a><a id="276" href="Categories.Diagram.Cone.html#276" class="Bound">F</a> <a id="278" class="Symbol">:</a> <a id="280" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="288" href="Categories.Diagram.Cone.html#252" class="Bound">J</a> <a id="290" href="Categories.Diagram.Cone.html#231" class="Bound">C</a><a id="291" class="Symbol">)</a> <a id="293" class="Keyword">where</a>
<a id="300" class="Keyword">open</a> <a id="305" href="Categories.Category.Core.html#442" class="Module">Category</a> <a id="314" href="Categories.Diagram.Cone.html#231" class="Bound">C</a>
<a id="316" class="Keyword">open</a> <a id="321" href="Categories.Functor.Core.html#248" class="Module">Functor</a> <a id="329" href="Categories.Diagram.Cone.html#276" class="Bound">F</a>
<a id="332" class="Keyword">open</a> <a id="337" class="Keyword">import</a> <a id="344" href="Level.html" class="Module">Level</a>
<a id="351" class="Keyword">record</a> <a id="Apex"></a><a id="358" href="Categories.Diagram.Cone.html#358" class="Record">Apex</a> <a id="363" class="Symbol">(</a><a id="364" href="Categories.Diagram.Cone.html#364" class="Bound">N</a> <a id="366" class="Symbol">:</a> <a id="368" href="Categories.Category.Core.html#559" class="Function">Obj</a><a id="371" class="Symbol">)</a> <a id="373" class="Symbol">:</a> <a id="375" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="379" class="Symbol">(</a><a id="380" href="Categories.Diagram.Cone.html#223" class="Bound">ℓ′</a> <a id="383" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="385" href="Categories.Diagram.Cone.html#220" class="Bound">o′</a> <a id="388" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="390" href="Categories.Diagram.Cone.html#216" class="Bound">e</a> <a id="392" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="394" href="Categories.Diagram.Cone.html#214" class="Bound">ℓ</a><a id="395" class="Symbol">)</a> <a id="397" class="Keyword">where</a>
<a id="405" class="Keyword">field</a>
<a id="Apex.ψ"></a><a id="415" href="Categories.Diagram.Cone.html#415" class="Field">ψ</a> <a id="423" class="Symbol">:</a> <a id="425" class="Symbol">(</a><a id="426" href="Categories.Diagram.Cone.html#426" class="Bound">X</a> <a id="428" class="Symbol">:</a> <a id="430" href="Categories.Category.Core.html#559" class="Field">Category.Obj</a> <a id="443" href="Categories.Diagram.Cone.html#252" class="Bound">J</a><a id="444" class="Symbol">)</a> <a id="446" class="Symbol">→</a> <a id="448" class="Symbol">(</a><a id="449" href="Categories.Diagram.Cone.html#364" class="Bound">N</a> <a id="451" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="453" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="456" href="Categories.Diagram.Cone.html#426" class="Bound">X</a><a id="457" class="Symbol">)</a>
<a id="Apex.commute"></a><a id="463" href="Categories.Diagram.Cone.html#463" class="Field">commute</a> <a id="471" class="Symbol">:</a> <a id="473" class="Symbol">∀</a> <a id="475" class="Symbol">{</a><a id="476" href="Categories.Diagram.Cone.html#476" class="Bound">X</a> <a id="478" href="Categories.Diagram.Cone.html#478" class="Bound">Y</a><a id="479" class="Symbol">}</a> <a id="481" class="Symbol">(</a><a id="482" href="Categories.Diagram.Cone.html#482" class="Bound">f</a> <a id="484" class="Symbol">:</a> <a id="486" href="Categories.Diagram.Cone.html#252" class="Bound">J</a> <a id="488" href="Categories.Category.html#502" class="Function Operator">[</a> <a id="490" href="Categories.Diagram.Cone.html#476" class="Bound">X</a> <a id="492" href="Categories.Category.html#502" class="Function Operator">,</a> <a id="494" href="Categories.Diagram.Cone.html#478" class="Bound">Y</a> <a id="496" href="Categories.Category.html#502" class="Function Operator">]</a><a id="497" class="Symbol">)</a> <a id="499" class="Symbol">→</a> <a id="501" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="504" href="Categories.Diagram.Cone.html#482" class="Bound">f</a> <a id="506" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="508" href="Categories.Diagram.Cone.html#415" class="Field">ψ</a> <a id="510" href="Categories.Diagram.Cone.html#476" class="Bound">X</a> <a id="512" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="514" href="Categories.Diagram.Cone.html#415" class="Field">ψ</a> <a id="516" href="Categories.Diagram.Cone.html#478" class="Bound">Y</a>
<a id="519" class="Keyword">record</a> <a id="Cone"></a><a id="526" href="Categories.Diagram.Cone.html#526" class="Record">Cone</a> <a id="531" class="Symbol">:</a> <a id="533" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="537" class="Symbol">(</a><a id="538" href="Categories.Diagram.Cone.html#212" class="Bound">o</a> <a id="540" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="542" href="Categories.Diagram.Cone.html#223" class="Bound">ℓ′</a> <a id="545" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="547" href="Categories.Diagram.Cone.html#220" class="Bound">o′</a> <a id="550" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="552" href="Categories.Diagram.Cone.html#216" class="Bound">e</a> <a id="554" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="556" href="Categories.Diagram.Cone.html#214" class="Bound">ℓ</a><a id="557" class="Symbol">)</a> <a id="559" class="Keyword">where</a>
<a id="567" class="Keyword">field</a>
<a id="577" class="Symbol">{</a><a id="Cone.N"></a><a id="578" href="Categories.Diagram.Cone.html#578" class="Field">N</a><a id="579" class="Symbol">}</a> <a id="582" class="Symbol">:</a> <a id="584" href="Categories.Category.Core.html#559" class="Function">Obj</a>
<a id="Cone.apex"></a><a id="592" href="Categories.Diagram.Cone.html#592" class="Field">apex</a> <a id="597" class="Symbol">:</a> <a id="599" href="Categories.Diagram.Cone.html#358" class="Record">Apex</a> <a id="604" href="Categories.Diagram.Cone.html#578" class="Field">N</a>
<a id="609" class="Keyword">open</a> <a id="614" href="Categories.Diagram.Cone.html#358" class="Module">Apex</a> <a id="619" href="Categories.Diagram.Cone.html#592" class="Field">apex</a> <a id="624" class="Keyword">public</a>
<a id="632" class="Keyword">open</a> <a id="637" href="Categories.Diagram.Cone.html#358" class="Module">Apex</a>
<a id="642" class="Keyword">open</a> <a id="647" href="Categories.Diagram.Cone.html#526" class="Module">Cone</a>
<a id="653" class="Keyword">record</a> <a id="Cone⇒"></a><a id="660" href="Categories.Diagram.Cone.html#660" class="Record">Cone⇒</a> <a id="666" class="Symbol">(</a><a id="667" href="Categories.Diagram.Cone.html#667" class="Bound">c</a> <a id="669" href="Categories.Diagram.Cone.html#669" class="Bound">c′</a> <a id="672" class="Symbol">:</a> <a id="674" href="Categories.Diagram.Cone.html#526" class="Record">Cone</a><a id="678" class="Symbol">)</a> <a id="680" class="Symbol">:</a> <a id="682" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="686" class="Symbol">(</a><a id="687" href="Categories.Diagram.Cone.html#214" class="Bound">ℓ</a> <a id="689" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="691" href="Categories.Diagram.Cone.html#216" class="Bound">e</a> <a id="693" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="695" href="Categories.Diagram.Cone.html#220" class="Bound">o′</a><a id="697" class="Symbol">)</a> <a id="699" class="Keyword">where</a>
<a id="707" class="Keyword">field</a>
<a id="Cone⇒.arr"></a><a id="717" href="Categories.Diagram.Cone.html#717" class="Field">arr</a> <a id="725" class="Symbol">:</a> <a id="727" href="Categories.Diagram.Cone.html#578" class="Field">N</a> <a id="729" href="Categories.Diagram.Cone.html#667" class="Bound">c</a> <a id="731" href="Categories.Category.Core.html#575" class="Function Operator">⇒</a> <a id="733" href="Categories.Diagram.Cone.html#578" class="Field">N</a> <a id="735" href="Categories.Diagram.Cone.html#669" class="Bound">c′</a>
<a id="Cone⇒.commute"></a><a id="742" href="Categories.Diagram.Cone.html#742" class="Field">commute</a> <a id="750" class="Symbol">:</a> <a id="752" class="Symbol">∀</a> <a id="754" class="Symbol">{</a><a id="755" href="Categories.Diagram.Cone.html#755" class="Bound">X</a><a id="756" class="Symbol">}</a> <a id="758" class="Symbol">→</a> <a id="760" href="Categories.Diagram.Cone.html#415" class="Field">ψ</a> <a id="762" href="Categories.Diagram.Cone.html#669" class="Bound">c′</a> <a id="765" href="Categories.Diagram.Cone.html#755" class="Bound">X</a> <a id="767" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="769" href="Categories.Diagram.Cone.html#717" class="Field">arr</a> <a id="773" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="775" href="Categories.Diagram.Cone.html#415" class="Field">ψ</a> <a id="777" href="Categories.Diagram.Cone.html#667" class="Bound">c</a> <a id="779" href="Categories.Diagram.Cone.html#755" class="Bound">X</a>
<a id="782" class="Keyword">open</a> <a id="787" href="Categories.Diagram.Cone.html#660" class="Module">Cone⇒</a>
</pre></body></html>
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