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<html><head><meta charset="utf-8"><title>Categories.Category.Monoidal.Instance.Setoids</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="37" class="Keyword">module</a> <a id="44" href="Categories.Category.Monoidal.Instance.Setoids.html" class="Module">Categories.Category.Monoidal.Instance.Setoids</a> <a id="90" class="Keyword">where</a>
<a id="97" class="Keyword">open</a> <a id="102" class="Keyword">import</a> <a id="109" href="Level.html" class="Module">Level</a> <a id="115" class="Keyword">using</a> <a id="121" class="Symbol">(</a><a id="122" href="Agda.Primitive.html#961" class="Primitive Operator">_⊔_</a><a id="125" class="Symbol">;</a> <a id="127" href="Agda.Primitive.html#931" class="Primitive">suc</a><a id="130" class="Symbol">)</a>
<a id="132" class="Keyword">open</a> <a id="137" class="Keyword">import</a> <a id="144" href="Data.Product.Base.html" class="Module">Data.Product.Base</a> <a id="162" class="Keyword">using</a> <a id="168" class="Symbol">(</a><a id="169" href="Data.Product.Base.html#636" class="Field">proj₁</a><a id="174" class="Symbol">;</a> <a id="176" href="Data.Product.Base.html#650" class="Field">proj₂</a><a id="181" class="Symbol">;</a> <a id="183" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">_,_</a><a id="186" class="Symbol">)</a>
<a id="188" class="Keyword">open</a> <a id="193" class="Keyword">import</a> <a id="200" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html" class="Module">Data.Product.Relation.Binary.Pointwise.NonDependent</a> <a id="252" class="Keyword">using</a> <a id="258" class="Symbol">(</a><a id="259" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">_×ₛ_</a><a id="263" class="Symbol">)</a>
<a id="265" class="Keyword">open</a> <a id="270" class="Keyword">import</a> <a id="277" href="Data.Product.Function.NonDependent.Setoid.html" class="Module">Data.Product.Function.NonDependent.Setoid</a> <a id="319" class="Keyword">using</a> <a id="325" class="Symbol">(</a><a id="326" href="Data.Product.Function.NonDependent.Setoid.html#766" class="Function">proj₁ₛ</a><a id="332" class="Symbol">;</a> <a id="334" href="Data.Product.Function.NonDependent.Setoid.html#838" class="Function">proj₂ₛ</a><a id="340" class="Symbol">;</a> <a id="342" href="Data.Product.Function.NonDependent.Setoid.html#910" class="Function Operator">&lt;_,_&gt;ₛ</a><a id="348" class="Symbol">)</a>
<a id="350" class="Keyword">open</a> <a id="355" class="Keyword">import</a> <a id="362" href="Data.Sum.Base.html" class="Module">Data.Sum.Base</a> <a id="376" class="Keyword">using</a> <a id="382" class="Symbol">(</a><a id="383" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a><a id="387" class="Symbol">;</a> <a id="389" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a><a id="393" class="Symbol">)</a>
<a id="395" class="Keyword">open</a> <a id="400" class="Keyword">import</a> <a id="407" href="Data.Sum.Relation.Binary.Pointwise.html" class="Module">Data.Sum.Relation.Binary.Pointwise</a> <a id="442" class="Keyword">using</a> <a id="448" class="Symbol">(</a><a id="449" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">_⊎ₛ_</a><a id="453" class="Symbol">)</a>
<a id="455" class="Keyword">open</a> <a id="460" class="Keyword">import</a> <a id="467" href="Data.Sum.Function.Setoid.html" class="Module">Data.Sum.Function.Setoid</a> <a id="492" class="Keyword">using</a> <a id="498" class="Symbol">(</a><a id="499" href="Data.Sum.Function.Setoid.html#868" class="Function">inj₁ₛ</a><a id="504" class="Symbol">;</a> <a id="506" href="Data.Sum.Function.Setoid.html#936" class="Function">inj₂ₛ</a><a id="511" class="Symbol">;</a> <a id="513" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">[_,_]ₛ</a><a id="519" class="Symbol">)</a>
<a id="521" class="Keyword">open</a> <a id="526" class="Keyword">import</a> <a id="533" href="Function.Bundles.html" class="Module">Function.Bundles</a> <a id="550" class="Keyword">using</a> <a id="556" class="Symbol">(</a><a id="557" href="Function.Bundles.html#15133" class="Function Operator">_⟨$⟩_</a><a id="562" class="Symbol">;</a> <a id="564" href="Function.Bundles.html#2043" class="Record">Func</a><a id="568" class="Symbol">)</a>
<a id="570" class="Keyword">open</a> <a id="575" class="Keyword">import</a> <a id="582" href="Relation.Binary.html" class="Module">Relation.Binary</a> <a id="598" class="Keyword">using</a> <a id="604" class="Symbol">(</a><a id="605" href="Relation.Binary.Bundles.html#1080" class="Record">Setoid</a><a id="611" class="Symbol">)</a>
<a id="614" class="Keyword">open</a> <a id="619" class="Keyword">import</a> <a id="626" href="Categories.Category.Core.html" class="Module">Categories.Category.Core</a> <a id="651" class="Keyword">using</a> <a id="657" class="Symbol">(</a><a id="658" href="Categories.Category.Core.html#442" class="Record">Category</a><a id="666" class="Symbol">)</a>
<a id="668" class="Keyword">open</a> <a id="673" class="Keyword">import</a> <a id="680" href="Categories.Category.Instance.Setoids.html" class="Module">Categories.Category.Instance.Setoids</a> <a id="717" class="Keyword">using</a> <a id="723" class="Symbol">(</a><a id="724" href="Categories.Category.Instance.Setoids.html#555" class="Function">Setoids</a><a id="731" class="Symbol">)</a>
<a id="733" class="Keyword">open</a> <a id="738" class="Keyword">import</a> <a id="745" href="Categories.Category.Cartesian.html" class="Module">Categories.Category.Cartesian</a> <a id="775" class="Keyword">using</a> <a id="781" class="Symbol">(</a><a id="782" href="Categories.Category.Cartesian.html#727" class="Record">Cartesian</a><a id="791" class="Symbol">)</a>
<a id="793" class="Keyword">open</a> <a id="798" class="Keyword">import</a> <a id="805" href="Categories.Category.Cartesian.Monoidal.html" class="Module">Categories.Category.Cartesian.Monoidal</a> <a id="844" class="Keyword">using</a> <a id="850" class="Symbol">(</a><a id="851" class="Keyword">module</a> <a id="858" href="Categories.Category.Cartesian.Monoidal.html#1139" class="Module">CartesianMonoidal</a><a id="875" class="Symbol">)</a>
<a id="877" class="Keyword">open</a> <a id="882" class="Keyword">import</a> <a id="889" href="Categories.Category.Cartesian.Bundle.html" class="Module">Categories.Category.Cartesian.Bundle</a> <a id="926" class="Keyword">using</a> <a id="932" class="Symbol">(</a><a id="933" href="Categories.Category.Cartesian.Bundle.html#422" class="Record">CartesianCategory</a><a id="950" class="Symbol">)</a>
<a id="952" class="Keyword">open</a> <a id="957" class="Keyword">import</a> <a id="964" href="Categories.Category.Cocartesian.html" class="Module">Categories.Category.Cocartesian</a> <a id="996" class="Keyword">using</a> <a id="1002" class="Symbol">(</a><a id="1003" href="Categories.Category.Cocartesian.html#3385" class="Record">Cocartesian</a><a id="1014" class="Symbol">)</a>
<a id="1016" class="Keyword">open</a> <a id="1021" class="Keyword">import</a> <a id="1028" href="Categories.Category.Instance.SingletonSet.html" class="Module">Categories.Category.Instance.SingletonSet</a> <a id="1070" class="Keyword">using</a> <a id="1076" class="Symbol">(</a><a id="1077" href="Categories.Category.Instance.SingletonSet.html#869" class="Function">SingletonSetoid-⊤</a><a id="1094" class="Symbol">)</a>
<a id="1096" class="Keyword">open</a> <a id="1101" class="Keyword">import</a> <a id="1108" href="Categories.Category.Instance.EmptySet.html" class="Module">Categories.Category.Instance.EmptySet</a> <a id="1146" class="Keyword">using</a> <a id="1152" class="Symbol">(</a><a id="1153" href="Categories.Category.Instance.EmptySet.html#941" class="Function">EmptySetoid-⊥</a><a id="1166" class="Symbol">)</a>
<a id="1169" class="Keyword">open</a> <a id="1174" href="Function.Bundles.html#2043" class="Module">Func</a>
<a id="1180" class="Keyword">module</a> <a id="1187" href="Categories.Category.Monoidal.Instance.Setoids.html#1187" class="Module">_</a> <a id="1189" class="Symbol">{</a><a id="1190" href="Categories.Category.Monoidal.Instance.Setoids.html#1190" class="Bound">o</a> <a id="1192" href="Categories.Category.Monoidal.Instance.Setoids.html#1192" class="Bound">ℓ</a><a id="1193" class="Symbol">}</a> <a id="1195" class="Keyword">where</a>
<a id="1204" href="Categories.Category.Monoidal.Instance.Setoids.html#1204" class="Function">Setoids-Cartesian</a> <a id="1222" class="Symbol">:</a> <a id="1224" href="Categories.Category.Cartesian.html#727" class="Record">Cartesian</a> <a id="1234" class="Symbol">(</a><a id="1235" href="Categories.Category.Instance.Setoids.html#555" class="Function">Setoids</a> <a id="1243" href="Categories.Category.Monoidal.Instance.Setoids.html#1190" class="Bound">o</a> <a id="1245" href="Categories.Category.Monoidal.Instance.Setoids.html#1192" class="Bound">ℓ</a><a id="1246" class="Symbol">)</a>
<a id="1250" href="Categories.Category.Monoidal.Instance.Setoids.html#1204" class="Function">Setoids-Cartesian</a> <a id="1268" class="Symbol">=</a> <a id="1270" class="Keyword">record</a>
<a id="1281" class="Symbol">{</a> <a id="1283" href="Categories.Category.Cartesian.html#777" class="Field">terminal</a> <a id="1292" class="Symbol">=</a> <a id="1294" href="Categories.Category.Instance.SingletonSet.html#869" class="Function">SingletonSetoid-⊤</a>
<a id="1316" class="Symbol">;</a> <a id="1318" href="Categories.Category.Cartesian.html#801" class="Field">products</a> <a id="1327" class="Symbol">=</a> <a id="1329" class="Keyword">record</a>
<a id="1342" class="Symbol">{</a> <a id="1344" href="Categories.Category.BinaryProducts.html#952" class="Field">product</a> <a id="1352" class="Symbol">=</a> <a id="1354" class="Symbol">λ</a> <a id="1356" class="Symbol">{</a><a id="1357" href="Categories.Category.Monoidal.Instance.Setoids.html#1357" class="Bound">A</a> <a id="1359" href="Categories.Category.Monoidal.Instance.Setoids.html#1359" class="Bound">B</a><a id="1360" class="Symbol">}</a> <a id="1362" class="Symbol">→</a>
<a id="1372" class="Keyword">let</a> <a id="1376" class="Keyword">module</a> <a id="1383" href="Categories.Category.Monoidal.Instance.Setoids.html#1383" class="Module">A</a> <a id="1385" class="Symbol">=</a> <a id="1387" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="1394" href="Categories.Category.Monoidal.Instance.Setoids.html#1357" class="Bound">A</a>
<a id="1408" class="Keyword">module</a> <a id="1415" href="Categories.Category.Monoidal.Instance.Setoids.html#1415" class="Module">B</a> <a id="1417" class="Symbol">=</a> <a id="1419" href="Relation.Binary.Bundles.html#1080" class="Module">Setoid</a> <a id="1426" href="Categories.Category.Monoidal.Instance.Setoids.html#1359" class="Bound">B</a>
<a id="1437" class="Keyword">in</a> <a id="1440" class="Keyword">record</a>
<a id="1457" class="Symbol">{</a> <a id="1459" href="Categories.Object.Product.Core.html#510" class="Field">A×B</a> <a id="1468" class="Symbol">=</a> <a id="1470" href="Categories.Category.Monoidal.Instance.Setoids.html#1357" class="Bound">A</a> <a id="1472" href="Data.Product.Relation.Binary.Pointwise.NonDependent.html#7083" class="Function Operator">×ₛ</a> <a id="1475" href="Categories.Category.Monoidal.Instance.Setoids.html#1359" class="Bound">B</a>
<a id="1487" class="Symbol">;</a> <a id="1489" href="Categories.Object.Product.Core.html#526" class="Field">π₁</a> <a id="1498" class="Symbol">=</a> <a id="1500" href="Data.Product.Function.NonDependent.Setoid.html#766" class="Function">proj₁ₛ</a>
<a id="1517" class="Symbol">;</a> <a id="1519" href="Categories.Object.Product.Core.html#546" class="Field">π₂</a> <a id="1528" class="Symbol">=</a> <a id="1530" href="Data.Product.Function.NonDependent.Setoid.html#838" class="Function">proj₂ₛ</a>
<a id="1547" class="Symbol">;</a> <a id="1549" href="Categories.Object.Product.Core.html#566" class="Field Operator">⟨_,_⟩</a> <a id="1558" class="Symbol">=</a> <a id="1560" class="Symbol">λ</a> <a id="1562" href="Categories.Category.Monoidal.Instance.Setoids.html#1562" class="Bound">f</a> <a id="1564" href="Categories.Category.Monoidal.Instance.Setoids.html#1564" class="Bound">g</a> <a id="1566" class="Symbol">→</a> <a id="1568" href="Data.Product.Function.NonDependent.Setoid.html#910" class="Function Operator">&lt;</a> <a id="1570" href="Categories.Category.Monoidal.Instance.Setoids.html#1562" class="Bound">f</a> <a id="1572" href="Data.Product.Function.NonDependent.Setoid.html#910" class="Function Operator">,</a> <a id="1574" href="Categories.Category.Monoidal.Instance.Setoids.html#1564" class="Bound">g</a> <a id="1576" href="Data.Product.Function.NonDependent.Setoid.html#910" class="Function Operator">&gt;ₛ</a>
<a id="1589" class="Symbol">;</a> <a id="1591" href="Categories.Object.Product.Core.html#603" class="Field">project₁</a> <a id="1600" class="Symbol">=</a> <a id="1602" href="Relation.Binary.Structures.html#1596" class="Function">A.refl</a>
<a id="1619" class="Symbol">;</a> <a id="1621" href="Categories.Object.Product.Core.html#637" class="Field">project₂</a> <a id="1630" class="Symbol">=</a> <a id="1632" href="Relation.Binary.Structures.html#1596" class="Function">B.refl</a>
<a id="1649" class="Symbol">;</a> <a id="1651" href="Categories.Object.Product.Core.html#671" class="Field">unique</a> <a id="1660" class="Symbol">=</a> <a id="1662" class="Symbol">λ</a> <a id="1664" href="Categories.Category.Monoidal.Instance.Setoids.html#1664" class="Bound">eq₁</a> <a id="1668" href="Categories.Category.Monoidal.Instance.Setoids.html#1668" class="Bound">eq₂</a> <a id="1672" class="Symbol">→</a> <a id="1674" href="Relation.Binary.Structures.html#1200" class="Function">A.sym</a> <a id="1680" href="Categories.Category.Monoidal.Instance.Setoids.html#1664" class="Bound">eq₁</a> <a id="1684" href="Agda.Builtin.Sigma.html#235" class="InductiveConstructor Operator">,</a> <a id="1686" href="Relation.Binary.Structures.html#1200" class="Function">B.sym</a> <a id="1692" href="Categories.Category.Monoidal.Instance.Setoids.html#1668" class="Bound">eq₂</a>
<a id="1706" class="Symbol">}</a>
<a id="1714" class="Symbol">}</a>
<a id="1720" class="Symbol">}</a>
<a id="1725" class="Keyword">module</a> <a id="1732" href="Categories.Category.Monoidal.Instance.Setoids.html#1732" class="Module">Setoids-Cartesian</a> <a id="1750" class="Symbol">=</a> <a id="1752" href="Categories.Category.Cartesian.html#727" class="Module">Cartesian</a> <a id="1762" href="Categories.Category.Monoidal.Instance.Setoids.html#1204" class="Function">Setoids-Cartesian</a>
<a id="1782" class="Keyword">open</a> <a id="1787" href="Categories.Category.Monoidal.Instance.Setoids.html#1732" class="Module">Setoids-Cartesian</a> <a id="1805" class="Keyword">public</a>
<a id="1814" class="Keyword">module</a> <a id="1821" href="Categories.Category.Monoidal.Instance.Setoids.html#1821" class="Module">Setoids-CartesianMonoidal</a> <a id="1847" class="Symbol">=</a> <a id="1849" href="Categories.Category.Cartesian.Monoidal.html#1139" class="Module">CartesianMonoidal</a> <a id="1867" href="Categories.Category.Monoidal.Instance.Setoids.html#1204" class="Function">Setoids-Cartesian</a>
<a id="1887" class="Keyword">open</a> <a id="1892" href="Categories.Category.Monoidal.Instance.Setoids.html#1821" class="Module">Setoids-CartesianMonoidal</a> <a id="1918" class="Keyword">renaming</a> <a id="1927" class="Symbol">(</a><a id="1928" href="Categories.Category.Cartesian.Monoidal.html#5400" class="Function">monoidal</a> <a id="1937" class="Symbol">to</a> <a id="1940" class="Function">Setoids-Monoidal</a><a id="1956" class="Symbol">)</a> <a id="1958" class="Keyword">public</a>
<a id="1968" href="Categories.Category.Monoidal.Instance.Setoids.html#1968" class="Function">Setoids-Cocartesian</a> <a id="1988" class="Symbol">:</a> <a id="1990" href="Categories.Category.Cocartesian.html#3385" class="Record">Cocartesian</a> <a id="2002" class="Symbol">(</a><a id="2003" href="Categories.Category.Instance.Setoids.html#555" class="Function">Setoids</a> <a id="2011" href="Categories.Category.Monoidal.Instance.Setoids.html#1190" class="Bound">o</a> <a id="2013" class="Symbol">(</a><a id="2014" href="Categories.Category.Monoidal.Instance.Setoids.html#1190" class="Bound">o</a> <a id="2016" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="2018" href="Categories.Category.Monoidal.Instance.Setoids.html#1192" class="Bound">ℓ</a><a id="2019" class="Symbol">))</a>
<a id="2024" href="Categories.Category.Monoidal.Instance.Setoids.html#1968" class="Function">Setoids-Cocartesian</a> <a id="2044" class="Symbol">=</a> <a id="2046" class="Keyword">record</a>
<a id="2057" class="Symbol">{</a> <a id="2059" href="Categories.Category.Cocartesian.html#3437" class="Field">initial</a> <a id="2067" class="Symbol">=</a> <a id="2069" href="Categories.Category.Instance.EmptySet.html#941" class="Function">EmptySetoid-⊥</a>
<a id="2087" class="Symbol">;</a> <a id="2089" href="Categories.Category.Cocartesian.html#3462" class="Field">coproducts</a> <a id="2100" class="Symbol">=</a> <a id="2102" class="Keyword">record</a>
<a id="2115" class="Symbol">{</a> <a id="2117" href="Categories.Category.Cocartesian.html#1450" class="Field">coproduct</a> <a id="2127" class="Symbol">=</a> <a id="2129" class="Symbol">λ</a> <a id="2131" class="Symbol">{</a><a id="2132" href="Categories.Category.Monoidal.Instance.Setoids.html#2132" class="Bound">A</a><a id="2133" class="Symbol">}</a> <a id="2135" class="Symbol">{</a><a id="2136" href="Categories.Category.Monoidal.Instance.Setoids.html#2136" class="Bound">B</a><a id="2137" class="Symbol">}</a> <a id="2139" class="Symbol">→</a> <a id="2141" class="Keyword">record</a>
<a id="2156" class="Symbol">{</a> <a id="2158" href="Categories.Object.Coproduct.html#476" class="Field">A+B</a> <a id="2162" class="Symbol">=</a> <a id="2164" href="Categories.Category.Monoidal.Instance.Setoids.html#2132" class="Bound">A</a> <a id="2166" href="Data.Sum.Relation.Binary.Pointwise.html#7477" class="Function Operator">⊎ₛ</a> <a id="2169" href="Categories.Category.Monoidal.Instance.Setoids.html#2136" class="Bound">B</a>
<a id="2179" class="Symbol">;</a> <a id="2181" href="Categories.Object.Coproduct.html#492" class="Field">i₁</a> <a id="2184" class="Symbol">=</a> <a id="2186" href="Data.Sum.Function.Setoid.html#868" class="Function">inj₁ₛ</a>
<a id="2200" class="Symbol">;</a> <a id="2202" href="Categories.Object.Coproduct.html#512" class="Field">i₂</a> <a id="2205" class="Symbol">=</a> <a id="2207" href="Data.Sum.Function.Setoid.html#936" class="Function">inj₂ₛ</a>
<a id="2221" class="Symbol">;</a> <a id="2223" href="Categories.Object.Coproduct.html#532" class="Field Operator">[_,_]</a> <a id="2229" class="Symbol">=</a> <a id="2231" class="Symbol">λ</a> <a id="2233" href="Categories.Category.Monoidal.Instance.Setoids.html#2233" class="Bound">f</a> <a id="2235" href="Categories.Category.Monoidal.Instance.Setoids.html#2235" class="Bound">g</a> <a id="2237" class="Symbol">→</a> <a id="2239" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">[</a> <a id="2241" href="Categories.Category.Monoidal.Instance.Setoids.html#2233" class="Bound">f</a> <a id="2243" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">,</a> <a id="2245" href="Categories.Category.Monoidal.Instance.Setoids.html#2235" class="Bound">g</a> <a id="2247" href="Data.Sum.Function.Setoid.html#1004" class="Function Operator">]ₛ</a>
<a id="2258" class="Symbol">;</a> <a id="2260" href="Categories.Object.Coproduct.html#569" class="Field">inject₁</a> <a id="2268" class="Symbol">=</a> <a id="2270" class="Symbol">λ</a> <a id="2272" class="Symbol">{</a><a id="2273" href="Categories.Category.Monoidal.Instance.Setoids.html#2273" class="Bound">C</a><a id="2274" class="Symbol">}</a> <a id="2276" class="Symbol">→</a> <a id="2278" href="Relation.Binary.Structures.html#1596" class="Function">Setoid.refl</a> <a id="2290" href="Categories.Category.Monoidal.Instance.Setoids.html#2273" class="Bound">C</a>
<a id="2300" class="Symbol">;</a> <a id="2302" href="Categories.Object.Coproduct.html#602" class="Field">inject₂</a> <a id="2310" class="Symbol">=</a> <a id="2312" class="Symbol">λ</a> <a id="2314" class="Symbol">{</a><a id="2315" href="Categories.Category.Monoidal.Instance.Setoids.html#2315" class="Bound">C</a><a id="2316" class="Symbol">}</a> <a id="2318" class="Symbol">→</a> <a id="2320" href="Relation.Binary.Structures.html#1596" class="Function">Setoid.refl</a> <a id="2332" href="Categories.Category.Monoidal.Instance.Setoids.html#2315" class="Bound">C</a>
<a id="2342" class="Symbol">;</a> <a id="2344" href="Categories.Object.Coproduct.html#635" class="Field">unique</a> <a id="2351" class="Symbol">=</a> <a id="2353" class="Symbol">λ</a> <a id="2355" class="Symbol">{</a><a id="2356" href="Categories.Category.Monoidal.Instance.Setoids.html#2356" class="Bound">C</a><a id="2357" class="Symbol">}</a> <a id="2359" href="Categories.Category.Monoidal.Instance.Setoids.html#2359" class="Bound">h₁≈f</a> <a id="2364" href="Categories.Category.Monoidal.Instance.Setoids.html#2364" class="Bound">h₂≈g</a> <a id="2369" class="Symbol">→</a> <a id="2371" class="Symbol">λ</a> <a id="2373" class="Symbol">{</a> <a id="2375" class="Symbol">{</a><a id="2376" href="Data.Sum.Base.html#675" class="InductiveConstructor">inj₁</a> <a id="2381" href="Categories.Category.Monoidal.Instance.Setoids.html#2381" class="Bound">x</a><a id="2382" class="Symbol">}</a> <a id="2384" class="Symbol">→</a> <a id="2386" href="Relation.Binary.Structures.html#1200" class="Function">Setoid.sym</a> <a id="2397" href="Categories.Category.Monoidal.Instance.Setoids.html#2356" class="Bound">C</a> <a id="2399" href="Categories.Category.Monoidal.Instance.Setoids.html#2359" class="Bound">h₁≈f</a>
<a id="2443" class="Symbol">;</a> <a id="2445" class="Symbol">{</a><a id="2446" href="Data.Sum.Base.html#700" class="InductiveConstructor">inj₂</a> <a id="2451" href="Categories.Category.Monoidal.Instance.Setoids.html#2451" class="Bound">y</a><a id="2452" class="Symbol">}</a> <a id="2454" class="Symbol">→</a> <a id="2456" href="Relation.Binary.Structures.html#1200" class="Function">Setoid.sym</a> <a id="2467" href="Categories.Category.Monoidal.Instance.Setoids.html#2356" class="Bound">C</a> <a id="2469" href="Categories.Category.Monoidal.Instance.Setoids.html#2364" class="Bound">h₂≈g</a><a id="2473" class="Symbol">}</a>
<a id="2483" class="Symbol">}</a>
<a id="2491" class="Symbol">}</a>
<a id="2497" class="Symbol">}</a>
<a id="Setoids-CartesianCategory"></a><a id="2500" href="Categories.Category.Monoidal.Instance.Setoids.html#2500" class="Function">Setoids-CartesianCategory</a> <a id="2526" class="Symbol">:</a> <a id="2528" class="Symbol">∀</a> <a id="2530" href="Categories.Category.Monoidal.Instance.Setoids.html#2530" class="Bound">c</a> <a id="2532" href="Categories.Category.Monoidal.Instance.Setoids.html#2532" class="Bound">ℓ</a> <a id="2534" class="Symbol">→</a> <a id="2536" href="Categories.Category.Cartesian.Bundle.html#422" class="Record">CartesianCategory</a> <a id="2554" class="Symbol">(</a><a id="2555" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="2559" class="Symbol">(</a><a id="2560" href="Categories.Category.Monoidal.Instance.Setoids.html#2530" class="Bound">c</a> <a id="2562" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="2564" href="Categories.Category.Monoidal.Instance.Setoids.html#2532" class="Bound">ℓ</a><a id="2565" class="Symbol">))</a> <a id="2568" class="Symbol">(</a><a id="2569" href="Categories.Category.Monoidal.Instance.Setoids.html#2530" class="Bound">c</a> <a id="2571" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="2573" href="Categories.Category.Monoidal.Instance.Setoids.html#2532" class="Bound">ℓ</a><a id="2574" class="Symbol">)</a> <a id="2576" class="Symbol">(</a><a id="2577" href="Categories.Category.Monoidal.Instance.Setoids.html#2530" class="Bound">c</a> <a id="2579" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="2581" href="Categories.Category.Monoidal.Instance.Setoids.html#2532" class="Bound">ℓ</a><a id="2582" class="Symbol">)</a>
<a id="2584" href="Categories.Category.Monoidal.Instance.Setoids.html#2500" class="Function">Setoids-CartesianCategory</a> <a id="2610" href="Categories.Category.Monoidal.Instance.Setoids.html#2610" class="Bound">c</a> <a id="2612" href="Categories.Category.Monoidal.Instance.Setoids.html#2612" class="Bound">ℓ</a> <a id="2614" class="Symbol">=</a> <a id="2616" class="Keyword">record</a>
<a id="2625" class="Symbol">{</a> <a id="2627" href="Categories.Category.Cartesian.Bundle.html#488" class="Field">U</a> <a id="2637" class="Symbol">=</a> <a id="2639" href="Categories.Category.Instance.Setoids.html#555" class="Function">Setoids</a> <a id="2647" href="Categories.Category.Monoidal.Instance.Setoids.html#2610" class="Bound">c</a> <a id="2649" href="Categories.Category.Monoidal.Instance.Setoids.html#2612" class="Bound">ℓ</a>
<a id="2653" class="Symbol">;</a> <a id="2655" href="Categories.Category.Cartesian.Bundle.html#540" class="Field">cartesian</a> <a id="2665" class="Symbol">=</a> <a id="2667" href="Categories.Category.Monoidal.Instance.Setoids.html#1204" class="Function">Setoids-Cartesian</a>
<a id="2687" class="Symbol">}</a>
</pre></body></html>
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