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bsc-leon-vatthauer/agda/bsc-thesis/Categories.Object.NaturalNumbers.html
Leon Vatthauer 2bf4655eae
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<!DOCTYPE HTML>
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<a id="1271" href="Categories.Object.NaturalNumbers.html#1271" class="Function">up-to-iso</a> <a id="1281" class="Symbol">:</a> <a id="1283" href="Categories.Object.NaturalNumbers.html#1112" class="Function">N.N</a> <a id="1287" href="Categories.Morphism.html#1958" class="Record Operator">≅</a> <a id="1289" href="Categories.Object.NaturalNumbers.html#1112" class="Field">N′.N</a>
<a id="1296" href="Categories.Object.NaturalNumbers.html#1271" class="Function">up-to-iso</a> <a id="1306" class="Symbol">=</a> <a id="1308" class="Keyword">record</a>
<a id="1319" class="Symbol">{</a> <a id="1321" href="Categories.Morphism.html#2006" class="Field">from</a> <a id="1326" class="Symbol">=</a> <a id="1328" href="Categories.Object.NaturalNumbers.html#492" class="Function">N.universal</a> <a id="1340" href="Categories.Object.NaturalNumbers.html#464" class="Function">N′.z</a> <a id="1345" href="Categories.Object.NaturalNumbers.html#478" class="Function">N′.s</a>
<a id="1354" class="Symbol">;</a> <a id="1356" href="Categories.Morphism.html#2023" class="Field">to</a> <a id="1359" class="Symbol">=</a> <a id="1361" href="Categories.Object.NaturalNumbers.html#492" class="Function">N′.universal</a> <a id="1374" href="Categories.Object.NaturalNumbers.html#464" class="Function">N.z</a> <a id="1378" href="Categories.Object.NaturalNumbers.html#478" class="Function">N.s</a>
<a id="1386" class="Symbol">;</a> <a id="1388" href="Categories.Morphism.html#2040" class="Field">iso</a> <a id="1392" class="Symbol">=</a> <a id="1394" class="Keyword">record</a>
<a id="1407" class="Symbol">{</a> <a id="1409" href="Categories.Morphism.html#1586" class="Field">isoˡ</a> <a id="1414" class="Symbol">=</a> <a id="1416" href="Categories.Object.NaturalNumbers.html#1495" class="Function">universal-∘</a> <a id="1428" href="Categories.Object.NaturalNumbers.html#1188" class="Bound">N</a> <a id="1430" href="Categories.Object.NaturalNumbers.html#1198" class="Bound">N′</a>
<a id="1439" class="Symbol">;</a> <a id="1441" href="Categories.Morphism.html#1612" class="Field">isoʳ</a> <a id="1446" class="Symbol">=</a> <a id="1448" href="Categories.Object.NaturalNumbers.html#1495" class="Function">universal-∘</a> <a id="1460" href="Categories.Object.NaturalNumbers.html#1198" class="Bound">N′</a> <a id="1463" href="Categories.Object.NaturalNumbers.html#1188" class="Bound">N</a>
<a id="1471" class="Symbol">}</a>
<a id="1477" class="Symbol">}</a>
<a id="1483" class="Keyword">where</a>
<a id="1495" href="Categories.Object.NaturalNumbers.html#1495" class="Function">universal-∘</a> <a id="1507" class="Symbol">:</a> <a id="1509" class="Symbol">∀</a> <a id="1511" class="Symbol">(</a><a id="1512" href="Categories.Object.NaturalNumbers.html#1512" class="Bound">N</a> <a id="1514" href="Categories.Object.NaturalNumbers.html#1514" class="Bound">N′</a> <a id="1517" class="Symbol">:</a> <a id="1519" href="Categories.Object.NaturalNumbers.html#1072" class="Record">NNO</a><a id="1522" class="Symbol">)</a> <a id="1524" class="Symbol">→</a> <a id="1526" href="Categories.Object.NaturalNumbers.html#492" class="Function">universal</a> <a id="1536" href="Categories.Object.NaturalNumbers.html#1514" class="Bound">N′</a> <a id="1539" class="Symbol">(</a><a id="1540" href="Categories.Object.NaturalNumbers.html#464" class="Function">z</a> <a id="1542" href="Categories.Object.NaturalNumbers.html#1512" class="Bound">N</a><a id="1543" class="Symbol">)</a> <a id="1545" class="Symbol">(</a><a id="1546" href="Categories.Object.NaturalNumbers.html#478" class="Function">s</a> <a id="1548" href="Categories.Object.NaturalNumbers.html#1512" class="Bound">N</a><a id="1549" class="Symbol">)</a> <a id="1551" href="Categories.Category.Core.html#656" class="Function Operator">∘</a> <a id="1553" href="Categories.Object.NaturalNumbers.html#492" class="Function">universal</a> <a id="1563" href="Categories.Object.NaturalNumbers.html#1512" class="Bound">N</a> <a id="1565" class="Symbol">(</a><a id="1566" href="Categories.Object.NaturalNumbers.html#464" class="Function">z</a> <a id="1568" href="Categories.Object.NaturalNumbers.html#1514" class="Bound">N′</a><a id="1570" class="Symbol">)</a> <a id="1572" class="Symbol">(</a><a id="1573" href="Categories.Object.NaturalNumbers.html#478" class="Function">s</a> <a id="1575" href="Categories.Object.NaturalNumbers.html#1514" class="Bound">N′</a><a id="1577" class="Symbol">)</a> <a id="1579" href="Categories.Category.Core.html#595" class="Function Operator">≈</a> <a id="1581" href="Categories.Category.Core.html#630" class="Function">id</a>
<a id="1592" href="Categories.Object.NaturalNumbers.html#1495" class="Function">universal-∘</a> <a id="1604" href="Categories.Object.NaturalNumbers.html#1604" class="Bound">N</a> <a id="1606" href="Categories.Object.NaturalNumbers.html#1606" class="Bound">N′</a> <a id="1609" class="Symbol">=</a> <a id="1611" href="Categories.Object.NaturalNumbers.html#694" class="Function">unique</a> <a id="1618" href="Categories.Object.NaturalNumbers.html#1604" class="Bound">N</a> <a id="1620" class="Symbol">(</a><a id="1621" href="Categories.Object.NaturalNumbers.html#538" class="Function">z-commute</a> <a id="1631" href="Categories.Object.NaturalNumbers.html#1606" class="Bound">N′</a> <a id="1634" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="1636" href="Categories.Morphism.Reasoning.Core.html#2347" class="Function">pushʳ</a> <a id="1642" class="Symbol">(</a><a id="1643" href="Categories.Object.NaturalNumbers.html#538" class="Function">z-commute</a> <a id="1653" href="Categories.Object.NaturalNumbers.html#1604" class="Bound">N</a><a id="1654" class="Symbol">))</a> <a id="1657" class="Symbol">(</a><a id="1658" href="Categories.Morphism.Reasoning.Core.html#2048" class="Function">pullˡ</a> <a id="1664" class="Symbol">(</a><a id="1665" href="Categories.Object.NaturalNumbers.html#608" class="Function">s-commute</a> <a id="1675" href="Categories.Object.NaturalNumbers.html#1606" class="Bound">N′</a><a id="1677" class="Symbol">)</a> <a id="1679" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="1681" href="Categories.Category.Core.html#715" class="Function">assoc</a> <a id="1687" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="1689" href="Categories.Category.Core.html#1706" class="Function">∘-resp-≈ʳ</a> <a id="1699" class="Symbol">(</a><a id="1700" href="Categories.Object.NaturalNumbers.html#608" class="Function">s-commute</a> <a id="1710" href="Categories.Object.NaturalNumbers.html#1604" class="Bound">N</a><a id="1711" class="Symbol">)</a> <a id="1713" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="1715" href="Categories.Category.Core.html#3005" class="Function">⟺</a> <a id="1717" href="Categories.Category.Core.html#715" class="Function">assoc</a><a id="1722" class="Symbol">)</a> <a id="1724" href="Categories.Category.Core.html#3061" class="Function Operator">○</a> <a id="1726" class="Symbol">(</a><a id="1727" href="Categories.Object.NaturalNumbers.html#799" class="Function">η</a> <a id="1729" href="Categories.Object.NaturalNumbers.html#1604" class="Bound">N</a><a id="1730" class="Symbol">)</a>
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