<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">o</font>, <font color="Maroon" title="c2">m</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>set </b><font color="Maroon" title="c3">1PCat</font> =  <a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font>;<br/>
<b>thus </b><a NAME="E1:80"/>
the <a href="cat_4.html#U5" title="CAT_4:sel.5">Initial</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> is <a href="cat_1.html#V8" title="CAT_1:attr.8">initial</a>
 <b>by </b><i><a class="ref" href="cat_4.html#T55" target="_self" title="CAT_4:th.55">Th55</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_4.html#D27" target="_self" title="CAT_4:def.27">CAT_4:def 27</a><br/>

<b>let </b><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span>;<br/>

<b>thus </b><a NAME="E2:80"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default">the <a href="cat_4.html#U7" title="CAT_4:sel.7">Incl1</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font>
 <b>by </b><i><a class="ref" href="cat_4.html#T49" target="_self" title="CAT_4:th.49">Th49</a></i>;<br/>

<b>thus </b><a NAME="E3:80"/>
 <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <span class="p1">(<span class="default">the <a href="cat_4.html#U8" title="CAT_4:sel.8">Incl2</a> of <span class="p2">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font>
 <b>by </b><i><a class="ref" href="cat_4.html#T49" target="_self" title="CAT_4:th.49">Th49</a></i>;<br/>

<b>thus </b><a NAME="E4:80"/>
the <a href="cat_4.html#U6" title="CAT_4:sel.6">Coproduct</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> <a href="cat_3.html#R4" title="CAT_3:pred.4">is_a_coproduct_wrt</a> the <a href="cat_4.html#U7" title="CAT_4:sel.7">Incl1</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>,the <a href="cat_4.html#U8" title="CAT_4:sel.8">Incl2</a> of <span class="p1">(<span class="default"><a href="cat_4.html#K23" title="CAT_4:func.23">c1Cat*</a> <font color="Maroon" title="c1">o</font>,<font color="Maroon" title="c2">m</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>
 <b>by </b><i><a class="ref" href="cat_4.html#T56" target="_self" title="CAT_4:th.56">Th56</a></i>;<br/>


</div>
