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

<b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">C'</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">D</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">S</font> be    <a href="cat_1.html#M2">Functor</a> of <span class="p1"><a href="cat_2.html#K11" target="_self">[:</a><span class="default"><font color="Maroon">C</font>,<font color="Maroon">C'</font></span><a href="cat_2.html#K11" target="_self">:]</a></span>,<font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">c</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">c'</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C'</font>;<br/>











<b>reconsider </b><font color="Maroon">S'</font> = <font color="Maroon">S</font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C</font>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">C'</font></span><a href="zfmisc_1.html#K2">:]</a></span>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">D</font> ;<br/>
<span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="cat_2.html#K15" target="_self">?-</a> <font color="Maroon">c</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c'</font></span>)</span> = 
<font color="Maroon">S</font> <a href="cat_2.html#K14" target="_self">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c'</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">c'</font></span><a href="cat_2.html#K12" target="_self">]</a></span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">S</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p2"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">c'</font></span><a href="cat_2.html#K12" target="_self">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T104">CAT_1:104</a></i>
;<br/>
<b>hence </b><a NAME="E3:51"/>
<span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <span class="p2">(<span class="default"><font color="Maroon">S</font> <a href="cat_2.html#K15" target="_self">?-</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="cat_1.html#K12">Obj</a> <font color="Maroon">S</font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1"><a href="cat_2.html#K12" target="_self">[</a><span class="default"><font color="Maroon">c</font>,<font color="Maroon">c'</font></span><a href="cat_2.html#K12" target="_self">]</a></span>
 <b>by </b><i><a class="ref" href="cat_1.html#T103">CAT_1:103</a></i>;<br/>


</div>
