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<html><head><meta charset="utf-8"><title>Categories.Object.Coproduct</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="IsCoproduct.inject₁"></a><a id="1270" href="Categories.Object.Coproduct.html#1270" class="Field">inject₁</a> <a id="1278" class="Symbol">:</a> <a id="1280" href="Categories.Object.Coproduct.html#1233" class="Field Operator">[</a> <a id="1282" href="Categories.Object.Coproduct.html#376" class="Generalizable">f</a> <a id="1284" href="Categories.Object.Coproduct.html#1233" class="Field Operator">,</a> <a id="1286" href="Categories.Object.Coproduct.html#378" class="Generalizable">g</a> <a id="1288" href="Categories.Object.Coproduct.html#1233" class="Field Operator">]</a> <a id="1290" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1292" href="Categories.Object.Coproduct.html#1168" class="Bound">i₁</a> <a id="1295" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1297" href="Categories.Object.Coproduct.html#376" class="Generalizable">f</a>
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<a id="1838" class="Symbol">}</a>
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<a id="1874" class="Keyword">module</a> <a id="1881" href="Categories.Object.Coproduct.html#1881" class="Module">_</a> <a id="1883" class="Symbol">{</a><a id="1884" href="Categories.Object.Coproduct.html#1884" class="Bound">A</a> <a id="1886" href="Categories.Object.Coproduct.html#1886" class="Bound">B</a> <a id="1888" class="Symbol">:</a> <a id="1890" href="Categories.Category.Core.html#559" class="Field">Obj</a><a id="1893" class="Symbol">}</a> <a id="1895" class="Keyword">where</a>
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<a id="5857" href="Categories.Object.Coproduct.html#5649" class="Function">Associative</a> <a id="5869" href="Categories.Object.Coproduct.html#5869" class="Bound">p₁</a> <a id="5872" href="Categories.Object.Coproduct.html#5872" class="Bound">p₂</a> <a id="5875" href="Categories.Object.Coproduct.html#5875" class="Bound">p₃</a> <a id="5878" href="Categories.Object.Coproduct.html#5878" class="Bound">p₄</a> <a id="5881" class="Symbol">=</a> <a id="5883" href="Categories.Object.Coproduct.html#2465" class="Function">up-to-iso</a> <a id="5893" class="Symbol">(</a><a id="5894" href="Categories.Object.Coproduct.html#3767" class="Function">Associable</a> <a id="5905" href="Categories.Object.Coproduct.html#5869" class="Bound">p₁</a> <a id="5908" href="Categories.Object.Coproduct.html#5872" class="Bound">p₂</a> <a id="5911" href="Categories.Object.Coproduct.html#5875" class="Bound">p₃</a><a id="5913" class="Symbol">)</a> <a id="5915" href="Categories.Object.Coproduct.html#5878" class="Bound">p₄</a>
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<a id="6552" class="Symbol">(_</a> <a id="6555" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6557" href="Categories.Morphism.html#2006" class="Field">from</a> <a id="6562" href="Categories.Object.Coproduct.html#6019" class="Bound">B₁≅B₂</a><a id="6567" class="Symbol">)</a> <a id="6569" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="6571" href="Categories.Morphism.html#2023" class="Field">to</a> <a id="6574" href="Categories.Object.Coproduct.html#6019" class="Bound">B₁≅B₂</a> <a id="6604" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="6607" href="Categories.Morphism.Reasoning.Core.html#6665" class="Function">cancelʳ</a> <a id="6615" class="Symbol">(</a><a id="6616" href="Categories.Morphism.html#1612" class="Function">isoʳ</a> <a id="6621" href="Categories.Object.Coproduct.html#6019" class="Bound">B₁≅B₂</a><a id="6626" class="Symbol">)</a> <a id="6628" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="6634" class="Symbol">_</a> <a id="6686" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="6690" class="Symbol">;</a> <a id="6692" href="Categories.Object.Coproduct.html#635" class="Field">unique</a> <a id="6706" class="Symbol">=</a> <a id="6708" class="Symbol">λ</a> <a id="6710" href="Categories.Object.Coproduct.html#6710" class="Bound">pfˡ</a> <a id="6714" href="Categories.Object.Coproduct.html#6714" class="Bound">pfʳ</a> <a id="6718" class="Symbol">→</a> <a id="6720" href="Categories.Object.Coproduct.html#635" class="Function">unique</a> <a id="6727" class="Symbol">(</a><a id="6728" href="Categories.Morphism.Reasoning.Iso.html#1094" class="Function">switch-fromtoʳ</a> <a id="6743" class="Symbol">(</a><a id="6744" href="Categories.Object.Coproduct.html#6908" class="Function">≅-sym</a> <a id="6750" href="Categories.Object.Coproduct.html#6013" class="Bound">A₁≅A₂</a><a id="6755" class="Symbol">)</a> <a id="6757" class="Symbol">((</a><a id="6759" href="Categories.Category.Core.html#715" class="Field">assoc</a> <a id="6765" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="6767" href="Categories.Object.Coproduct.html#6710" class="Bound">pfˡ</a><a id="6770" class="Symbol">)))</a> <a id="6774" class="Symbol">(</a><a id="6775" href="Categories.Morphism.Reasoning.Iso.html#1094" class="Function">switch-fromtoʳ</a> <a id="6790" class="Symbol">(</a><a id="6791" href="Categories.Object.Coproduct.html#6908" class="Function">≅-sym</a> <a id="6797" href="Categories.Object.Coproduct.html#6019" class="Bound">B₁≅B₂</a><a id="6802" class="Symbol">)</a> <a id="6804" class="Symbol">((</a><a id="6806" href="Categories.Category.Core.html#715" class="Field">assoc</a> <a id="6812" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="6814" href="Categories.Object.Coproduct.html#6714" class="Bound">pfʳ</a><a id="6817" class="Symbol">)))</a>
<a id="6823" class="Symbol">}</a>
<a id="6827" class="Keyword">where</a> <a id="6833" class="Keyword">open</a> <a id="6838" href="Categories.Object.Coproduct.html#398" class="Module">Coproduct</a> <a id="6848" href="Categories.Object.Coproduct.html#6011" class="Bound">p</a>
<a id="6858" class="Keyword">open</a> <a id="6863" href="Categories.Morphism.html#1958" class="Module Operator">_≅_</a>
<a id="6875" class="Keyword">open</a> <a id="6880" href="Categories.Morphism.html#3269" class="Module">≅</a> <a id="6882" class="Keyword">using</a> <a id="6888" class="Symbol">()</a> <a id="6891" class="Keyword">renaming</a> <a id="6900" class="Symbol">(</a><a id="6901" href="Relation.Binary.Structures.html#1603" class="Function">sym</a> <a id="6905" class="Symbol">to</a> <a id="6908" class="Function">≅-sym</a><a id="6913" class="Symbol">)</a>
</pre></body></html>
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