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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">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>given </b><font color="Maroon">F</font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font><b> such that </b><a NAME="E1:24"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">F</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">G</font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">C</font>,<font color="Maroon">D</font><b> such that </b><a NAME="E2:24"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">G</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">F</font>,<font color="Maroon">G</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">F</font> is <a href="funct_1.html#V2">one-to-one</a> &amp; <font color="Maroon">G</font> 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>;<br/>
<b>hence </b><a NAME="E4:24"/>
<span class="p1"><a href="cat_2.html#K20">[:</a><span class="default"><font color="Maroon">F</font>,<font color="Maroon">G</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/>; <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">F</font>,<font color="Maroon">G</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">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">G</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">B</font>,<span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">G</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i>, </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">B</font>,<font color="Maroon">D</font></span><a href="cat_2.html#K11">:]</a></span>
<b>by </b><i><a class="ref" href="isocat_1.html#T1" target="_self">Th1</a>, </i>
;<br/>


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