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<b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">a</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>, <font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>;<br/>







<b>assume </b><a NAME="E1:32"/><i><font color="Green">E7</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E2:32"/><i><font color="Green">E8</font></i>: 
(  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a</font>,<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">b</font> <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#T56">CAT_1:56</a></i>;<br/>
<b>let </b><font color="Maroon">f</font> be    <a href="cat_1.html#M1">Morphism</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>

<b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" target="_self">id</a> <font color="Maroon">F</font></span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">b</font></span>)</span> <a href="cat_1.html#K9">*</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font>
<b>by </b><i>, <a class="ref" href="cat_1.html#T57">CAT_1:57</a></i>
<br/>.= 
<font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="cat_1.html#K9">*</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="cat_1.html#T58">CAT_1:58</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <span class="p2">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i>, , </i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="cat_1.html#K13">.</a> <font color="Maroon">a</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="nattra_1.html#K3" target="_self">.</a> <font color="Maroon">f</font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K4" target="_self">id</a> <font color="Maroon">F</font></span>)</span> <a href="nattra_1.html#K5" target="_self">.</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i/>
;<br/>


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