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26 lines
8.8 KiB
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<html><head><meta charset="utf-8"><title>Categories.Morphism.Notation</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">{-
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Useful notation for Epimorphisms, Mononmorphisms, and isomorphisms
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-}</a>
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<a id="112" class="Keyword">module</a> <a id="119" href="Categories.Morphism.Notation.html" class="Module">Categories.Morphism.Notation</a> <a id="148" class="Keyword">where</a>
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<a id="155" class="Keyword">open</a> <a id="160" class="Keyword">import</a> <a id="167" href="Level.html" class="Module">Level</a>
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<a id="174" class="Keyword">open</a> <a id="179" class="Keyword">import</a> <a id="186" href="Categories.Category.Core.html" class="Module">Categories.Category.Core</a>
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<a id="211" class="Keyword">open</a> <a id="216" class="Keyword">import</a> <a id="223" href="Categories.Morphism.html" class="Module">Categories.Morphism</a>
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<a id="244" class="Keyword">private</a>
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<a id="254" class="Keyword">variable</a>
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<a id="267" href="Categories.Morphism.Notation.html#267" class="Generalizable">o</a> <a id="269" href="Categories.Morphism.Notation.html#269" class="Generalizable">ℓ</a> <a id="271" href="Categories.Morphism.Notation.html#271" class="Generalizable">e</a> <a id="273" class="Symbol">:</a> <a id="275" href="Agda.Primitive.html#742" class="Postulate">Level</a>
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<a id="_[_↣_]"></a><a id="282" href="Categories.Morphism.Notation.html#282" class="Function Operator">_[_↣_]</a> <a id="289" class="Symbol">:</a> <a id="291" class="Symbol">(</a><a id="292" href="Categories.Morphism.Notation.html#292" class="Bound">𝒞</a> <a id="294" class="Symbol">:</a> <a id="296" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="305" href="Categories.Morphism.Notation.html#267" class="Generalizable">o</a> <a id="307" href="Categories.Morphism.Notation.html#269" class="Generalizable">ℓ</a> <a id="309" href="Categories.Morphism.Notation.html#271" class="Generalizable">e</a><a id="310" class="Symbol">)</a> <a id="312" class="Symbol">→</a> <a id="314" class="Symbol">(</a><a id="315" href="Categories.Morphism.Notation.html#315" class="Bound">A</a> <a id="317" href="Categories.Morphism.Notation.html#317" class="Bound">B</a> <a id="319" class="Symbol">:</a> <a id="321" href="Categories.Category.Core.html#559" class="Field">Category.Obj</a> <a id="334" href="Categories.Morphism.Notation.html#292" class="Bound">𝒞</a><a id="335" class="Symbol">)</a> <a id="337" class="Symbol">→</a> <a id="339" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="343" class="Symbol">(</a><a id="344" href="Categories.Morphism.Notation.html#267" class="Generalizable">o</a> <a id="346" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="348" href="Categories.Morphism.Notation.html#269" class="Generalizable">ℓ</a> <a id="350" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="352" href="Categories.Morphism.Notation.html#271" class="Generalizable">e</a><a id="353" class="Symbol">)</a>
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<a id="355" href="Categories.Morphism.Notation.html#355" class="Bound">𝒞</a> <a id="357" href="Categories.Morphism.Notation.html#282" class="Function Operator">[</a> <a id="359" href="Categories.Morphism.Notation.html#359" class="Bound">A</a> <a id="361" href="Categories.Morphism.Notation.html#282" class="Function Operator">↣</a> <a id="363" href="Categories.Morphism.Notation.html#363" class="Bound">B</a> <a id="365" href="Categories.Morphism.Notation.html#282" class="Function Operator">]</a> <a id="367" class="Symbol">=</a> <a id="369" href="Categories.Morphism.html#789" class="Record Operator">_↣_</a> <a id="373" href="Categories.Morphism.Notation.html#355" class="Bound">𝒞</a> <a id="375" href="Categories.Morphism.Notation.html#359" class="Bound">A</a> <a id="377" href="Categories.Morphism.Notation.html#363" class="Bound">B</a>
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<a id="_[_↠_]"></a><a id="380" href="Categories.Morphism.Notation.html#380" class="Function Operator">_[_↠_]</a> <a id="387" class="Symbol">:</a> <a id="389" class="Symbol">(</a><a id="390" href="Categories.Morphism.Notation.html#390" class="Bound">𝒞</a> <a id="392" class="Symbol">:</a> <a id="394" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="403" href="Categories.Morphism.Notation.html#267" class="Generalizable">o</a> <a id="405" href="Categories.Morphism.Notation.html#269" class="Generalizable">ℓ</a> <a id="407" href="Categories.Morphism.Notation.html#271" class="Generalizable">e</a><a id="408" class="Symbol">)</a> <a id="410" class="Symbol">→</a> <a id="412" class="Symbol">(</a><a id="413" href="Categories.Morphism.Notation.html#413" class="Bound">A</a> <a id="415" href="Categories.Morphism.Notation.html#415" class="Bound">B</a> <a id="417" class="Symbol">:</a> <a id="419" href="Categories.Category.Core.html#559" class="Field">Category.Obj</a> <a id="432" href="Categories.Morphism.Notation.html#390" class="Bound">𝒞</a><a id="433" class="Symbol">)</a> <a id="435" class="Symbol">→</a> <a id="437" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="441" class="Symbol">(</a><a id="442" href="Categories.Morphism.Notation.html#267" class="Generalizable">o</a> <a id="444" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="446" href="Categories.Morphism.Notation.html#269" class="Generalizable">ℓ</a> <a id="448" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="450" href="Categories.Morphism.Notation.html#271" class="Generalizable">e</a><a id="451" class="Symbol">)</a>
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<a id="453" href="Categories.Morphism.Notation.html#453" class="Bound">𝒞</a> <a id="455" href="Categories.Morphism.Notation.html#380" class="Function Operator">[</a> <a id="457" href="Categories.Morphism.Notation.html#457" class="Bound">A</a> <a id="459" href="Categories.Morphism.Notation.html#380" class="Function Operator">↠</a> <a id="461" href="Categories.Morphism.Notation.html#461" class="Bound">B</a> <a id="463" href="Categories.Morphism.Notation.html#380" class="Function Operator">]</a> <a id="465" class="Symbol">=</a> <a id="467" href="Categories.Morphism.html#1154" class="Record Operator">_↠_</a> <a id="471" href="Categories.Morphism.Notation.html#453" class="Bound">𝒞</a> <a id="473" href="Categories.Morphism.Notation.html#457" class="Bound">A</a> <a id="475" href="Categories.Morphism.Notation.html#461" class="Bound">B</a>
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<a id="_[_≅_]"></a><a id="478" href="Categories.Morphism.Notation.html#478" class="Function Operator">_[_≅_]</a> <a id="485" class="Symbol">:</a> <a id="487" class="Symbol">(</a><a id="488" href="Categories.Morphism.Notation.html#488" class="Bound">𝒞</a> <a id="490" class="Symbol">:</a> <a id="492" href="Categories.Category.Core.html#442" class="Record">Category</a> <a id="501" href="Categories.Morphism.Notation.html#267" class="Generalizable">o</a> <a id="503" href="Categories.Morphism.Notation.html#269" class="Generalizable">ℓ</a> <a id="505" href="Categories.Morphism.Notation.html#271" class="Generalizable">e</a><a id="506" class="Symbol">)</a> <a id="508" class="Symbol">→</a> <a id="510" class="Symbol">(</a><a id="511" href="Categories.Morphism.Notation.html#511" class="Bound">A</a> <a id="513" href="Categories.Morphism.Notation.html#513" class="Bound">B</a> <a id="515" class="Symbol">:</a> <a id="517" href="Categories.Category.Core.html#559" class="Field">Category.Obj</a> <a id="530" href="Categories.Morphism.Notation.html#488" class="Bound">𝒞</a><a id="531" class="Symbol">)</a> <a id="533" class="Symbol">→</a> <a id="535" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="539" class="Symbol">(</a><a id="540" href="Categories.Morphism.Notation.html#269" class="Generalizable">ℓ</a> <a id="542" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="544" href="Categories.Morphism.Notation.html#271" class="Generalizable">e</a><a id="545" class="Symbol">)</a>
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<a id="547" href="Categories.Morphism.Notation.html#547" class="Bound">𝒞</a> <a id="549" href="Categories.Morphism.Notation.html#478" class="Function Operator">[</a> <a id="551" href="Categories.Morphism.Notation.html#551" class="Bound">A</a> <a id="553" href="Categories.Morphism.Notation.html#478" class="Function Operator">≅</a> <a id="555" href="Categories.Morphism.Notation.html#555" class="Bound">B</a> <a id="557" href="Categories.Morphism.Notation.html#478" class="Function Operator">]</a> <a id="559" class="Symbol">=</a> <a id="561" href="Categories.Morphism.html#1958" class="Record Operator">_≅_</a> <a id="565" href="Categories.Morphism.Notation.html#547" class="Bound">𝒞</a> <a id="567" href="Categories.Morphism.Notation.html#551" class="Bound">A</a> <a id="569" href="Categories.Morphism.Notation.html#555" class="Bound">B</a>
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</pre></body></html>
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