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<b>let </b><font color="Maroon">A</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F1</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>, <font color="Maroon">F2</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/>





<b>assume </b><a NAME="E1:16"/><i><font color="Green">E7</font></i>: 
for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>  st  <a href="cat_1.html#K6">Hom</a> <font color="Olive">a</font>,<font color="Olive">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">f</font> being   <a href="cat_1.html#M1">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font> holds  <font color="Maroon">F1</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Olive">f</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">A</font>;<br/><b>reconsider </b><font color="Maroon">f'</font> = <font color="Maroon">f</font> as    <a href="cat_1.html#M1">Morphism</a> of  <a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font>, <a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font> <b>by </b><i><a class="ref" href="cat_1.html#T22">CAT_1:22</a></i>;<br/><a NAME="E2:16_1"/><i><font color="Green">E8</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K2">dom</a> <font color="Maroon">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K3">cod</a> <font color="Maroon">f</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="cat_1.html#T19">CAT_1:19</a></i>;<br/><b>hence </b><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font> = 
<font color="Maroon">F1</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f'</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F2</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f'</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font>
<b>by </b><i>, </i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:16"/>
<font color="Maroon">F1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">F2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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