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<html><head><meta charset="utf-8"><title>Categories.Diagram.Coequalizer</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="1165" href="Categories.Diagram.Coequalizer.html#1073" class="Bound">h</a> <a id="1185" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1188" href="Categories.Diagram.Coequalizer.html#576" class="Field">universal</a> <a id="1198" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="1204" href="Categories.Diagram.Coequalizer.html#523" class="Field">coequalize</a> <a id="1215" href="Categories.Diagram.Coequalizer.html#1090" class="Bound">eq</a> <a id="1218" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1220" href="Categories.Diagram.Coequalizer.html#439" class="Bound">arr</a> <a id="1224" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="IsCoequalizer.coequalize-resp-≈′"></a><a id="1229" href="Categories.Diagram.Coequalizer.html#1229" class="Function">coequalize-resp-≈′</a> <a id="1248" class="Symbol">:</a> <a id="1250" class="Symbol">(</a><a id="1251" href="Categories.Diagram.Coequalizer.html#1251" class="Bound">eq</a> <a id="1254" class="Symbol">:</a> <a id="1257" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="1259" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1261" href="Categories.Diagram.Coequalizer.html#425" class="Bound">f</a> <a id="1263" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1265" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="1267" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1269" href="Categories.Diagram.Coequalizer.html#427" class="Bound">g</a><a id="1270" class="Symbol">)</a> <a id="1272" class="Symbol">→</a> <a id="1274" class="Symbol">(</a><a id="1275" href="Categories.Diagram.Coequalizer.html#1275" class="Bound">eq′</a> <a id="1279" class="Symbol">:</a> <a id="1281" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a> <a id="1283" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1285" href="Categories.Diagram.Coequalizer.html#425" class="Bound">f</a> <a id="1287" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1289" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a> <a id="1291" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="1293" href="Categories.Diagram.Coequalizer.html#427" class="Bound">g</a><a id="1294" class="Symbol">)</a> <a id="1296" class="Symbol">→</a>
<a id="1302" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="1304" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1306" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a> <a id="1308" class="Symbol">→</a> <a id="1310" href="Categories.Diagram.Coequalizer.html#386" class="Generalizable">j</a> <a id="1312" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1314" href="Categories.Diagram.Coequalizer.html#523" class="Field">coequalize</a> <a id="1325" href="Categories.Diagram.Coequalizer.html#1251" class="Bound">eq</a> <a id="1328" class="Symbol">→</a> <a id="1330" href="Categories.Diagram.Coequalizer.html#388" class="Generalizable">k</a> <a id="1332" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1334" href="Categories.Diagram.Coequalizer.html#523" class="Field">coequalize</a> <a id="1345" href="Categories.Diagram.Coequalizer.html#1275" class="Bound">eq′</a> <a id="1349" class="Symbol">→</a> <a id="1351" href="Categories.Diagram.Coequalizer.html#386" class="Generalizable">j</a> <a id="1353" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="1355" href="Categories.Diagram.Coequalizer.html#388" class="Generalizable">k</a>
<a id="1359" href="Categories.Diagram.Coequalizer.html#1229" class="Function">coequalize-resp-≈′</a> <a id="1378" class="Symbol">{</a><a id="1379" class="Argument">j</a> <a id="1381" class="Symbol">=</a> <a id="1383" href="Categories.Diagram.Coequalizer.html#1383" class="Bound">j</a><a id="1384" class="Symbol">}</a> <a id="1386" class="Symbol">{</a><a id="1387" class="Argument">k</a> <a id="1389" class="Symbol">=</a> <a id="1391" href="Categories.Diagram.Coequalizer.html#1391" class="Bound">k</a><a id="1392" class="Symbol">}</a> <a id="1394" href="Categories.Diagram.Coequalizer.html#1394" class="Bound">eq</a> <a id="1397" href="Categories.Diagram.Coequalizer.html#1397" class="Bound">eq′</a> <a id="1401" href="Categories.Diagram.Coequalizer.html#1401" class="Bound">h≈i</a> <a id="1405" href="Categories.Diagram.Coequalizer.html#1405" class="Bound">eqj</a> <a id="1409" href="Categories.Diagram.Coequalizer.html#1409" class="Bound">eqk</a> <a id="1413" class="Symbol">=</a> <a id="1415" href="Relation.Binary.Reasoning.Base.Single.html#1925" class="Function Operator">begin</a>
<a id="1425" href="Categories.Diagram.Coequalizer.html#1383" class="Bound">j</a> <a id="1440" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1443" href="Categories.Diagram.Coequalizer.html#1405" class="Bound">eqj</a> <a id="1447" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="1453" href="Categories.Diagram.Coequalizer.html#523" class="Field">coequalize</a> <a id="1464" href="Categories.Diagram.Coequalizer.html#1394" class="Bound">eq</a> <a id="1468" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">≈⟨</a> <a id="1471" href="Categories.Diagram.Coequalizer.html#937" class="Function">coequalize-resp-≈</a> <a id="1489" href="Categories.Diagram.Coequalizer.html#1401" class="Bound">h≈i</a> <a id="1493" href="Relation.Binary.Reasoning.Setoid.html#1061" class="Function">⟩</a>
<a id="1499" href="Categories.Diagram.Coequalizer.html#523" class="Field">coequalize</a> <a id="1510" href="Categories.Diagram.Coequalizer.html#1397" class="Bound">eq′</a> <a id="1514" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">≈˘⟨</a> <a id="1518" href="Categories.Diagram.Coequalizer.html#1409" class="Bound">eqk</a> <a id="1522" href="Relation.Binary.Reasoning.Setoid.html#1162" class="Function">⟩</a>
<a id="1528" href="Categories.Diagram.Coequalizer.html#1391" class="Bound">k</a> <a id="1543" href="Relation.Binary.Reasoning.Base.Single.html#2564" class="Function Operator">∎</a>
<a id="1546" class="Comment">-- This could be proved via duality, but is easier to just write by hand,</a>
<a id="1620" class="Comment">-- as it makes the dependency graph a lot cleaner.</a>
<a id="IsCoequalizer⇒Epi"></a><a id="1671" href="Categories.Diagram.Coequalizer.html#1671" class="Function">IsCoequalizer⇒Epi</a> <a id="1689" class="Symbol">:</a> <a id="1691" href="Categories.Diagram.Coequalizer.html#406" class="Record">IsCoequalizer</a> <a id="1705" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="1707" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a> <a id="1709" href="Categories.Diagram.Coequalizer.html#386" class="Generalizable">j</a> <a id="1711" class="Symbol">→</a> <a id="1713" href="Categories.Morphism.html#875" class="Function">Epi</a> <a id="1717" href="Categories.Diagram.Coequalizer.html#386" class="Generalizable">j</a>
<a id="1719" href="Categories.Diagram.Coequalizer.html#1671" class="Function">IsCoequalizer⇒Epi</a> <a id="1737" href="Categories.Diagram.Coequalizer.html#1737" class="Bound">coeq</a> <a id="1742" class="Symbol">_</a> <a id="1744" class="Symbol">_</a> <a id="1746" href="Categories.Diagram.Coequalizer.html#1746" class="Bound">eq</a> <a id="1749" class="Symbol">=</a>
<a id="1753" href="Categories.Diagram.Coequalizer.html#1229" class="Function">coequalize-resp-≈′</a> <a id="1772" class="Symbol">(</a><a id="1773" href="Categories.Morphism.Reasoning.Core.html#3392" class="Function">extendˡ</a> <a id="1781" href="Categories.Diagram.Coequalizer.html#488" class="Function">equality</a><a id="1789" class="Symbol">)</a> <a id="1791" class="Symbol">(</a><a id="1792" href="Categories.Morphism.Reasoning.Core.html#3392" class="Function">extendˡ</a> <a id="1800" href="Categories.Diagram.Coequalizer.html#488" class="Function">equality</a><a id="1808" class="Symbol">)</a> <a id="1810" href="Categories.Diagram.Coequalizer.html#1746" class="Bound">eq</a> <a id="1813" class="Symbol">(</a><a id="1814" href="Categories.Diagram.Coequalizer.html#652" class="Function">unique</a> <a id="1821" href="Relation.Binary.Structures.html#1577" class="Function">refl</a><a id="1825" class="Symbol">)</a> <a id="1827" class="Symbol">(</a><a id="1828" href="Categories.Diagram.Coequalizer.html#652" class="Function">unique</a> <a id="1835" href="Relation.Binary.Structures.html#1577" class="Function">refl</a><a id="1839" class="Symbol">)</a>
<a id="1843" class="Keyword">where</a>
<a id="1853" class="Keyword">open</a> <a id="1858" href="Categories.Diagram.Coequalizer.html#406" class="Module">IsCoequalizer</a> <a id="1872" href="Categories.Diagram.Coequalizer.html#1737" class="Bound">coeq</a>
<a id="1878" class="Keyword">record</a> <a id="Coequalizer"></a><a id="1885" href="Categories.Diagram.Coequalizer.html#1885" class="Record">Coequalizer</a> <a id="1897" class="Symbol">(</a><a id="1898" href="Categories.Diagram.Coequalizer.html#1898" class="Bound">f</a> <a id="1900" href="Categories.Diagram.Coequalizer.html#1900" class="Bound">g</a> <a id="1902" class="Symbol">:</a> <a id="1904" href="Categories.Diagram.Coequalizer.html#366" class="Generalizable">A</a> <a id="1906" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="1908" href="Categories.Diagram.Coequalizer.html#368" class="Generalizable">B</a><a id="1909" class="Symbol">)</a> <a id="1911" class="Symbol">:</a> <a id="1913" href="Agda.Primitive.html#320" class="Primitive">Set</a> <a id="1917" class="Symbol">(</a><a id="1918" href="Categories.Diagram.Coequalizer.html#131" class="Bound">o</a> <a id="1920" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1922" href="Categories.Diagram.Coequalizer.html#133" class="Bound">ℓ</a> <a id="1924" href="Agda.Primitive.html#804" class="Primitive Operator">⊔</a> <a id="1926" href="Categories.Diagram.Coequalizer.html#135" class="Bound">e</a><a id="1927" class="Symbol">)</a> <a id="1929" class="Keyword">where</a>
<a id="1937" class="Keyword">field</a>
<a id="1947" class="Symbol">{</a><a id="Coequalizer.obj"></a><a id="1948" href="Categories.Diagram.Coequalizer.html#1948" class="Field">obj</a><a id="1951" class="Symbol">}</a> <a id="1953" class="Symbol">:</a> <a id="1955" href="Categories.Category.Core.html#559" class="Field">Obj</a>
<a id="Coequalizer.arr"></a><a id="1963" href="Categories.Diagram.Coequalizer.html#1963" class="Field">arr</a> <a id="1969" class="Symbol">:</a> <a id="1971" href="Categories.Diagram.Coequalizer.html#1908" class="Bound">B</a> <a id="1973" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="1975" href="Categories.Diagram.Coequalizer.html#1948" class="Field">obj</a>
<a id="Coequalizer.isCoequalizer"></a><a id="1983" href="Categories.Diagram.Coequalizer.html#1983" class="Field">isCoequalizer</a> <a id="1997" class="Symbol">:</a> <a id="1999" href="Categories.Diagram.Coequalizer.html#406" class="Record">IsCoequalizer</a> <a id="2013" href="Categories.Diagram.Coequalizer.html#1898" class="Bound">f</a> <a id="2015" href="Categories.Diagram.Coequalizer.html#1900" class="Bound">g</a> <a id="2017" href="Categories.Diagram.Coequalizer.html#1963" class="Field">arr</a>
<a id="2024" class="Keyword">open</a> <a id="2029" href="Categories.Diagram.Coequalizer.html#406" class="Module">IsCoequalizer</a> <a id="2043" href="Categories.Diagram.Coequalizer.html#1983" class="Field">isCoequalizer</a> <a id="2057" class="Keyword">public</a>
<a id="Coequalizer⇒Epi"></a><a id="2065" href="Categories.Diagram.Coequalizer.html#2065" class="Function">Coequalizer⇒Epi</a> <a id="2081" class="Symbol">:</a> <a id="2083" class="Symbol">(</a><a id="2084" href="Categories.Diagram.Coequalizer.html#2084" class="Bound">e</a> <a id="2086" class="Symbol">:</a> <a id="2088" href="Categories.Diagram.Coequalizer.html#1885" class="Record">Coequalizer</a> <a id="2100" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="2102" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a><a id="2103" class="Symbol">)</a> <a id="2105" class="Symbol">→</a> <a id="2107" href="Categories.Morphism.html#875" class="Function">Epi</a> <a id="2111" class="Symbol">(</a><a id="2112" href="Categories.Diagram.Coequalizer.html#1963" class="Field">Coequalizer.arr</a> <a id="2128" href="Categories.Diagram.Coequalizer.html#2084" class="Bound">e</a><a id="2129" class="Symbol">)</a>
<a id="2131" href="Categories.Diagram.Coequalizer.html#2065" class="Function">Coequalizer⇒Epi</a> <a id="2147" href="Categories.Diagram.Coequalizer.html#2147" class="Bound">coeq</a> <a id="2152" class="Symbol">=</a> <a id="2154" href="Categories.Diagram.Coequalizer.html#1671" class="Function">IsCoequalizer⇒Epi</a> <a id="2172" href="Categories.Diagram.Coequalizer.html#1983" class="Function">isCoequalizer</a>
<a id="2188" class="Keyword">where</a>
<a id="2198" class="Keyword">open</a> <a id="2203" href="Categories.Diagram.Coequalizer.html#1885" class="Module">Coequalizer</a> <a id="2215" href="Categories.Diagram.Coequalizer.html#2147" class="Bound">coeq</a>
<a id="2221" class="Comment">-- Proving this via duality arguments is kind of annoying, as ≅ does not behave nicely in</a>
<a id="2311" class="Comment">-- concert with op.</a>
<a id="up-to-iso"></a><a id="2331" href="Categories.Diagram.Coequalizer.html#2331" class="Function">up-to-iso</a> <a id="2341" class="Symbol">:</a> <a id="2343" class="Symbol">(</a><a id="2344" href="Categories.Diagram.Coequalizer.html#2344" class="Bound">coe₁</a> <a id="2349" href="Categories.Diagram.Coequalizer.html#2349" class="Bound">coe₂</a> <a id="2354" class="Symbol">:</a> <a id="2356" href="Categories.Diagram.Coequalizer.html#1885" class="Record">Coequalizer</a> <a id="2368" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="2370" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a><a id="2371" class="Symbol">)</a> <a id="2373" class="Symbol">→</a> <a id="2375" href="Categories.Diagram.Coequalizer.html#1948" class="Field">Coequalizer.obj</a> <a id="2391" href="Categories.Diagram.Coequalizer.html#2344" class="Bound">coe₁</a> <a id="2396" href="Categories.Morphism.html#1958" class="Record Operator">≅</a> <a id="2398" href="Categories.Diagram.Coequalizer.html#1948" class="Field">Coequalizer.obj</a> <a id="2414" href="Categories.Diagram.Coequalizer.html#2349" class="Bound">coe₂</a>
<a id="2419" href="Categories.Diagram.Coequalizer.html#2331" class="Function">up-to-iso</a> <a id="2429" href="Categories.Diagram.Coequalizer.html#2429" class="Bound">coe₁</a> <a id="2434" href="Categories.Diagram.Coequalizer.html#2434" class="Bound">coe₂</a> <a id="2439" class="Symbol">=</a> <a id="2441" class="Keyword">record</a>
<a id="2450" class="Symbol">{</a> <a id="2452" href="Categories.Morphism.html#2006" class="Field">from</a> <a id="2457" class="Symbol">=</a> <a id="2459" href="Categories.Diagram.Coequalizer.html#2637" class="Function">repack</a> <a id="2466" href="Categories.Diagram.Coequalizer.html#2429" class="Bound">coe₁</a> <a id="2471" href="Categories.Diagram.Coequalizer.html#2434" class="Bound">coe₂</a>
<a id="2478" class="Symbol">;</a> <a id="2480" href="Categories.Morphism.html#2023" class="Field">to</a> <a id="2483" class="Symbol">=</a> <a id="2485" href="Categories.Diagram.Coequalizer.html#2637" class="Function">repack</a> <a id="2492" href="Categories.Diagram.Coequalizer.html#2434" class="Bound">coe₂</a> <a id="2497" href="Categories.Diagram.Coequalizer.html#2429" class="Bound">coe₁</a>
<a id="2504" class="Symbol">;</a> <a id="2506" href="Categories.Morphism.html#2040" class="Field">iso</a> <a id="2510" class="Symbol">=</a> <a id="2512" class="Keyword">record</a>
<a id="2523" class="Symbol">{</a> <a id="2525" href="Categories.Morphism.html#1586" class="Field">isoˡ</a> <a id="2530" class="Symbol">=</a> <a id="2532" href="Categories.Diagram.Coequalizer.html#3041" class="Function">repack-cancel</a> <a id="2546" href="Categories.Diagram.Coequalizer.html#2434" class="Bound">coe₂</a> <a id="2551" href="Categories.Diagram.Coequalizer.html#2429" class="Bound">coe₁</a>
<a id="2560" class="Symbol">;</a> <a id="2562" href="Categories.Morphism.html#1612" class="Field">isoʳ</a> <a id="2567" class="Symbol">=</a> <a id="2569" href="Categories.Diagram.Coequalizer.html#3041" class="Function">repack-cancel</a> <a id="2583" href="Categories.Diagram.Coequalizer.html#2429" class="Bound">coe₁</a> <a id="2588" href="Categories.Diagram.Coequalizer.html#2434" class="Bound">coe₂</a>
<a id="2597" class="Symbol">}</a>
<a id="2601" class="Symbol">}</a>
<a id="2605" class="Keyword">where</a>
<a id="2615" class="Keyword">open</a> <a id="2620" href="Categories.Diagram.Coequalizer.html#1885" class="Module">Coequalizer</a>
<a id="2637" href="Categories.Diagram.Coequalizer.html#2637" class="Function">repack</a> <a id="2644" class="Symbol">:</a> <a id="2646" class="Symbol">(</a><a id="2647" href="Categories.Diagram.Coequalizer.html#2647" class="Bound">coe₁</a> <a id="2652" href="Categories.Diagram.Coequalizer.html#2652" class="Bound">coe₂</a> <a id="2657" class="Symbol">:</a> <a id="2659" href="Categories.Diagram.Coequalizer.html#1885" class="Record">Coequalizer</a> <a id="2671" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="2673" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a><a id="2674" class="Symbol">)</a> <a id="2676" class="Symbol">→</a> <a id="2678" href="Categories.Diagram.Coequalizer.html#1948" class="Field">obj</a> <a id="2682" href="Categories.Diagram.Coequalizer.html#2647" class="Bound">coe₁</a> <a id="2687" href="Categories.Category.Core.html#575" class="Field Operator">⇒</a> <a id="2689" href="Categories.Diagram.Coequalizer.html#1948" class="Field">obj</a> <a id="2693" href="Categories.Diagram.Coequalizer.html#2652" class="Bound">coe₂</a>
<a id="2702" href="Categories.Diagram.Coequalizer.html#2637" class="Function">repack</a> <a id="2709" href="Categories.Diagram.Coequalizer.html#2709" class="Bound">coe₁</a> <a id="2714" href="Categories.Diagram.Coequalizer.html#2714" class="Bound">coe₂</a> <a id="2719" class="Symbol">=</a> <a id="2721" href="Categories.Diagram.Coequalizer.html#523" class="Function">coequalize</a> <a id="2732" href="Categories.Diagram.Coequalizer.html#2709" class="Bound">coe₁</a> <a id="2737" class="Symbol">(</a><a id="2738" href="Categories.Diagram.Coequalizer.html#488" class="Function">equality</a> <a id="2747" href="Categories.Diagram.Coequalizer.html#2714" class="Bound">coe₂</a><a id="2751" class="Symbol">)</a>
<a id="2758" href="Categories.Diagram.Coequalizer.html#2758" class="Function">repack∘</a> <a id="2766" class="Symbol">:</a> <a id="2768" class="Symbol">(</a><a id="2769" href="Categories.Diagram.Coequalizer.html#2769" class="Bound">coe₁</a> <a id="2774" href="Categories.Diagram.Coequalizer.html#2774" class="Bound">coe₂</a> <a id="2779" href="Categories.Diagram.Coequalizer.html#2779" class="Bound">coe₃</a> <a id="2784" class="Symbol">:</a> <a id="2786" href="Categories.Diagram.Coequalizer.html#1885" class="Record">Coequalizer</a> <a id="2798" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="2800" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a><a id="2801" class="Symbol">)</a> <a id="2803" class="Symbol">→</a> <a id="2805" href="Categories.Diagram.Coequalizer.html#2637" class="Function">repack</a> <a id="2812" href="Categories.Diagram.Coequalizer.html#2774" class="Bound">coe₂</a> <a id="2817" href="Categories.Diagram.Coequalizer.html#2779" class="Bound">coe₃</a> <a id="2822" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="2824" href="Categories.Diagram.Coequalizer.html#2637" class="Function">repack</a> <a id="2831" href="Categories.Diagram.Coequalizer.html#2769" class="Bound">coe₁</a> <a id="2836" href="Categories.Diagram.Coequalizer.html#2774" class="Bound">coe₂</a> <a id="2841" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="2843" href="Categories.Diagram.Coequalizer.html#2637" class="Function">repack</a> <a id="2850" href="Categories.Diagram.Coequalizer.html#2769" class="Bound">coe₁</a> <a id="2855" href="Categories.Diagram.Coequalizer.html#2779" class="Bound">coe₃</a>
<a id="2864" href="Categories.Diagram.Coequalizer.html#2758" class="Function">repack∘</a> <a id="2872" href="Categories.Diagram.Coequalizer.html#2872" class="Bound">coe₁</a> <a id="2877" href="Categories.Diagram.Coequalizer.html#2877" class="Bound">coe₂</a> <a id="2882" href="Categories.Diagram.Coequalizer.html#2882" class="Bound">coe₃</a> <a id="2887" class="Symbol">=</a> <a id="2889" href="Categories.Diagram.Coequalizer.html#652" class="Function">unique</a> <a id="2896" href="Categories.Diagram.Coequalizer.html#2872" class="Bound">coe₁</a> <a id="2901" class="Symbol">(</a><a id="2902" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="2904" class="Symbol">(</a><a id="2905" href="Categories.Morphism.Reasoning.Core.html#6339" class="Function">glueTrianglesˡ</a> <a id="2920" class="Symbol">(</a><a id="2921" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="2923" class="Symbol">(</a><a id="2924" href="Categories.Diagram.Coequalizer.html#576" class="Function">universal</a> <a id="2934" href="Categories.Diagram.Coequalizer.html#2877" class="Bound">coe₂</a><a id="2938" class="Symbol">))</a> <a id="2941" class="Symbol">(</a><a id="2942" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="2944" class="Symbol">(</a><a id="2945" href="Categories.Diagram.Coequalizer.html#576" class="Function">universal</a> <a id="2955" href="Categories.Diagram.Coequalizer.html#2872" class="Bound">coe₁</a><a id="2959" class="Symbol">))))</a> <a id="2964" class="Comment">-- unique e₃ (⟺ (glueTrianglesʳ (⟺ (universal e₃)) (⟺ (universal e₂))))</a>
<a id="3041" href="Categories.Diagram.Coequalizer.html#3041" class="Function">repack-cancel</a> <a id="3055" class="Symbol">:</a> <a id="3057" class="Symbol">(</a><a id="3058" href="Categories.Diagram.Coequalizer.html#3058" class="Bound">e₁</a> <a id="3061" href="Categories.Diagram.Coequalizer.html#3061" class="Bound">e₂</a> <a id="3064" class="Symbol">:</a> <a id="3066" href="Categories.Diagram.Coequalizer.html#1885" class="Record">Coequalizer</a> <a id="3078" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="3080" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a><a id="3081" class="Symbol">)</a> <a id="3083" class="Symbol">→</a> <a id="3085" href="Categories.Diagram.Coequalizer.html#2637" class="Function">repack</a> <a id="3092" href="Categories.Diagram.Coequalizer.html#3058" class="Bound">e₁</a> <a id="3095" href="Categories.Diagram.Coequalizer.html#3061" class="Bound">e₂</a> <a id="3098" href="Categories.Category.Core.html#656" class="Field Operator">∘</a> <a id="3100" href="Categories.Diagram.Coequalizer.html#2637" class="Function">repack</a> <a id="3107" href="Categories.Diagram.Coequalizer.html#3061" class="Bound">e₂</a> <a id="3110" href="Categories.Diagram.Coequalizer.html#3058" class="Bound">e₁</a> <a id="3113" href="Categories.Category.Core.html#595" class="Field Operator">≈</a> <a id="3115" href="Categories.Category.Core.html#630" class="Field">id</a>
<a id="3122" href="Categories.Diagram.Coequalizer.html#3041" class="Function">repack-cancel</a> <a id="3136" href="Categories.Diagram.Coequalizer.html#3136" class="Bound">coe₁</a> <a id="3141" href="Categories.Diagram.Coequalizer.html#3141" class="Bound">coe₂</a> <a id="3146" class="Symbol">=</a> <a id="3148" href="Categories.Diagram.Coequalizer.html#2758" class="Function">repack∘</a> <a id="3156" href="Categories.Diagram.Coequalizer.html#3141" class="Bound">coe₂</a> <a id="3161" href="Categories.Diagram.Coequalizer.html#3136" class="Bound">coe₁</a> <a id="3166" href="Categories.Diagram.Coequalizer.html#3141" class="Bound">coe₂</a> <a id="3171" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="3173" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="3175" class="Symbol">(</a><a id="3176" href="Categories.Diagram.Coequalizer.html#854" class="Function">id-coequalize</a> <a id="3190" href="Categories.Diagram.Coequalizer.html#3141" class="Bound">coe₂</a><a id="3194" class="Symbol">)</a>
<a id="IsCoequalizer⇒Coequalizer"></a><a id="3197" href="Categories.Diagram.Coequalizer.html#3197" class="Function">IsCoequalizer⇒Coequalizer</a> <a id="3223" class="Symbol">:</a> <a id="3225" href="Categories.Diagram.Coequalizer.html#406" class="Record">IsCoequalizer</a> <a id="3239" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="3241" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a> <a id="3243" href="Categories.Diagram.Coequalizer.html#388" class="Generalizable">k</a> <a id="3245" class="Symbol">→</a> <a id="3247" href="Categories.Diagram.Coequalizer.html#1885" class="Record">Coequalizer</a> <a id="3259" href="Categories.Diagram.Coequalizer.html#382" class="Generalizable">h</a> <a id="3261" href="Categories.Diagram.Coequalizer.html#384" class="Generalizable">i</a>
<a id="3263" href="Categories.Diagram.Coequalizer.html#3197" class="Function">IsCoequalizer⇒Coequalizer</a> <a id="3289" class="Symbol">{</a><a id="3290" class="Argument">k</a> <a id="3292" class="Symbol">=</a> <a id="3294" href="Categories.Diagram.Coequalizer.html#3294" class="Bound">k</a><a id="3295" class="Symbol">}</a> <a id="3297" href="Categories.Diagram.Coequalizer.html#3297" class="Bound">is-coe</a> <a id="3304" class="Symbol">=</a> <a id="3306" class="Keyword">record</a>
<a id="3315" class="Symbol">{</a> <a id="3317" href="Categories.Diagram.Coequalizer.html#1963" class="Field">arr</a> <a id="3321" class="Symbol">=</a> <a id="3323" href="Categories.Diagram.Coequalizer.html#3294" class="Bound">k</a>
<a id="3327" class="Symbol">;</a> <a id="3329" href="Categories.Diagram.Coequalizer.html#1983" class="Field">isCoequalizer</a> <a id="3343" class="Symbol">=</a> <a id="3345" href="Categories.Diagram.Coequalizer.html#3297" class="Bound">is-coe</a>
<a id="3354" class="Symbol">}</a>
</pre></body></html>
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