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</pre>
<h1 id="free-elgot-algebras">Free Elgot algebras</h1>
<p>A free elgot algebra is a free object in the category of Elgot
algebras.</p>
<pre class="Agda"> <a id="elgotForgetfulF"></a><a id="1197" href="Algebra.Elgot.Free.html#1197" class="Function">elgotForgetfulF</a> <a id="1213" class="Symbol">:</a> <a id="1215" href="Categories.Functor.Core.html#248" class="Record">Functor</a> <a id="1223" href="Category.Construction.ElgotAlgebras.html#939" class="Function">Elgot-Algebras</a> <a id="1238" href="Algebra.Elgot.Free.html#773" class="Bound">C</a>
<a id="1242" href="Algebra.Elgot.Free.html#1197" class="Function">elgotForgetfulF</a> <a id="1258" class="Symbol">=</a> <a id="1260" class="Keyword">record</a>
<a id="1271" class="Symbol">{</a> <a id="1273" href="Categories.Functor.Core.html#432" class="Field">F₀</a> <a id="1276" class="Symbol">=</a> <a id="1278" class="Symbol">λ</a> <a id="1280" href="Algebra.Elgot.Free.html#1280" class="Bound">X</a> <a id="1282" class="Symbol">→</a> <a id="1284" href="Algebra.Elgot.html#16018" class="Field">Elgot-Algebra.A</a> <a id="1300" href="Algebra.Elgot.Free.html#1280" class="Bound">X</a>
<a id="1306" class="Symbol">;</a> <a id="1308" href="Categories.Functor.Core.html#455" class="Field">F₁</a> <a id="1311" class="Symbol">=</a> <a id="1313" class="Symbol">λ</a> <a id="1315" href="Algebra.Elgot.Free.html#1315" class="Bound">f</a> <a id="1317" class="Symbol">→</a> <a id="1319" href="Category.Construction.ElgotAlgebras.html#794" class="Field">Elgot-Algebra-Morphism.h</a> <a id="1344" href="Algebra.Elgot.Free.html#1315" class="Bound">f</a>
<a id="1350" class="Symbol">;</a> <a id="1352" href="Categories.Functor.Core.html#511" class="Field">identity</a> <a id="1361" class="Symbol">=</a> <a id="1363" href="Relation.Binary.Structures.html#1596" class="Function">refl</a>
<a id="1372" class="Symbol">;</a> <a id="1374" href="Categories.Functor.Core.html#565" class="Field">homomorphism</a> <a id="1387" class="Symbol">=</a> <a id="1389" href="Relation.Binary.Structures.html#1596" class="Function">refl</a>
<a id="1398" class="Symbol">;</a> <a id="1400" href="Categories.Functor.Core.html#696" class="Field">F-resp-≈</a> <a id="1409" class="Symbol">=</a> <a id="1411" class="Symbol">λ</a> <a id="1413" href="Algebra.Elgot.Free.html#1413" class="Bound">x</a> <a id="1415" class="Symbol">→</a> <a id="1417" href="Algebra.Elgot.Free.html#1413" class="Bound">x</a>
<a id="1423" class="Symbol">}</a>
<a id="1428" class="Comment">-- typedef</a>
<a id="FreeElgotAlgebra"></a><a id="1441" href="Algebra.Elgot.Free.html#1441" class="Function">FreeElgotAlgebra</a> <a id="1458" class="Symbol">:</a> <a id="1460" href="Categories.Category.Core.html#559" class="Function">Obj</a> <a id="1464" class="Symbol">→</a> <a id="1466" href="Agda.Primitive.html#388" class="Primitive">Set</a> <a id="1470" class="Symbol">(</a><a id="1471" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1475" href="Algebra.Elgot.Free.html#765" class="Bound">o</a> <a id="1477" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1479" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1483" href="Algebra.Elgot.Free.html#767" class="Bound">ℓ</a> <a id="1485" href="Agda.Primitive.html#961" class="Primitive Operator">⊔</a> <a id="1487" href="Agda.Primitive.html#931" class="Primitive">suc</a> <a id="1491" href="Algebra.Elgot.Free.html#769" class="Bound">e</a><a id="1492" class="Symbol">)</a>
<a id="1496" href="Algebra.Elgot.Free.html#1441" class="Function">FreeElgotAlgebra</a> <a id="1513" href="Algebra.Elgot.Free.html#1513" class="Bound">X</a> <a id="1515" class="Symbol">=</a> <a id="1517" href="Categories.FreeObjects.Free.html#485" class="Record">FreeObject</a> <a id="1528" class="Symbol">{</a><a id="1529" class="Argument">C</a> <a id="1531" class="Symbol">=</a> <a id="1533" href="Algebra.Elgot.Free.html#773" class="Bound">C</a><a id="1534" class="Symbol">}</a> <a id="1536" class="Symbol">{</a><a id="1537" class="Argument">D</a> <a id="1539" class="Symbol">=</a> <a id="1541" href="Category.Construction.ElgotAlgebras.html#939" class="Function">Elgot-Algebras</a><a id="1555" class="Symbol">}</a> <a id="1557" href="Algebra.Elgot.Free.html#1197" class="Function">elgotForgetfulF</a> <a id="1573" href="Algebra.Elgot.Free.html#1513" class="Bound">X</a>
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