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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/>







<b>given </b><font color="Maroon">c<sub>5</sub></font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><a NAME="E1:24"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="isocat_1.html#NR1" target="_self">is_an_isomorphism</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D4" target="_self">ISOCAT_1:def 4</a><br/>

<b>given </b><font color="Maroon">c<sub>6</sub></font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font><b> such that </b><a NAME="E2:24"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="isocat_1.html#NR1" target="_self">is_an_isomorphism</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D4" target="_self">ISOCAT_1:def 4</a><br/>

<b>take </b>
<span class="p1"><a href="cat_2.html#K20">[:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="cat_2.html#K20">:]</a></span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D4" target="_self">ISOCAT_1:def 4</a><br/>

<a NAME="E3:24"/>
( <font color="Maroon">c<sub>5</sub></font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">c<sub>6</sub></font> is <a href="funct_1.html#V2">one-to-one</a> )
 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:24"><i><font color="Green">E16</font></i></a>, <a class="txt" href="isocat_1.html#E2:24"><i><font color="Green">E17</font></i></a>, <a class="ref" href="isocat_1.html#D3" target="_self">Def3</a></i>;<br/>
<b>hence </b><a NAME="E4:24"/>
<span class="p1"><a href="cat_2.html#K20">[:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="cat_2.html#K20">:]</a></span> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i><a class="ref" href="isocat_1.html#T1" target="_self">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D3" target="_self">ISOCAT_1:def 3</a><br/>

<b>thus </b> <a href="relset_1.html#K5">rng</a> <span class="p1"><a href="cat_2.html#K20">[:</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="cat_2.html#K20">:]</a></span> = 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="ref" href="funct_3.html#T88">FUNCT_3:88</a></i>
<br/>.= 
<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<sub>2</sub></font>,<span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="txt" href="isocat_1.html#E1:24"><i><font color="Green">E16</font></i></a>, <a class="ref" href="isocat_1.html#D3" target="_self">Def3</a></i>
<br/>.= 
<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<sub>2</sub></font>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">c<sub>4</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="txt" href="isocat_1.html#E2:24"><i><font color="Green">E17</font></i></a>, <a class="ref" href="isocat_1.html#D3" target="_self">Def3</a></i>
<br/>.= 
the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="cat_2.html#K11">:]</a></span>

;<br/>


</div>
