<?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">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">C</font>;<br/>



<a NAME="E1:57"/><i><font color="Green">E20</font></i>: 
 <a href="cat_1.html#K6" target="_self">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/>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="57_1"><b>now </b></a><div class="add"><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">g1</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">b</font>,<font color="Maroon">c</font>, <font color="Maroon">g2</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">b</font>,<font color="Maroon">c</font>;<br/><b>assume </b><a NAME="E1:57_1"/>
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><a NAME="E2:57_1"/><b>then </b>
( <font color="Maroon">g1</font> <a href="cat_1.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" target="_self">id</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g1</font> &amp; <font color="Maroon">g2</font> <a href="cat_1.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" target="_self">id</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:57_1"/>
( <font color="Maroon">g1</font> <a href="cat_1.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" target="_self">id</a> <font color="Maroon">b</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> <a href="cat_1.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10" target="_self">id</a> <font color="Maroon">b</font></span>)</span> implies <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g2</font> )
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:57"/>
 <a href="cat_1.html#K10" target="_self">id</a> <font color="Maroon">b</font> is <a href="cat_1.html#V4" target="_self">epi</a>
 <b>by </b><i><a class="ref" href="cat_1.html#T18" target="_self">Th18</a>, </i>;<br/>


</div>
