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<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">T</font> be    <a href="cat_1.html#M2" target="_self">Functor</a> of <font color="Maroon">C</font>,<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>, <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">f</font> be    <a href="hidden.html#M1">set</a> ;<br/>









<b>assume </b><a NAME="E1:101"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">c</font>,<font color="Maroon">c'</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font> as    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">c</font>,<font color="Maroon">c'</font> <b>by </b><i/>;<br/>
<a NAME="E3:101"/>
(  <a href="cat_1.html#K2" target="_self">dom</a> <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c</font> &amp;  <a href="cat_1.html#K3" target="_self">cod</a> <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">c'</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:101"/><b>then </b>
( <font color="Maroon">T</font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K2" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f'</font></span>)</span> &amp; <font color="Maroon">T</font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c'</font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K3" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f'</font></span>)</span> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:101"/>
<font color="Maroon">T</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6" target="_self">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">c'</font></span>)</span>
 ;<br/>


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