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



<b>given </b><font color="Maroon">c<sub>3</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="E1:57"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">c<sub>3</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>
<font color="Maroon">c<sub>3</sub></font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D10" target="_self">ISOCAT_1:def 10</a><br/>

<b>take </b>
<font color="Maroon">c<sub>3</sub></font> <a href="isocat_1.html#K1" target="_self">"</a> 
;<br/>

<b>thus </b><a NAME="E2:57"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="isocat_1.html#K1" target="_self">"</a> </span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="nattra_1.html#NR4" target="_self">~=</a>  <a href="cat_1.html#K15">id</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="cat_1.html#K14">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="isocat_1.html#K1" target="_self">"</a> </span>)</span> <a href="nattra_1.html#NR4" target="_self">~=</a>  <a href="cat_1.html#K15">id</a> <font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="txt" href="isocat_1.html#E1:57"><i><font color="Green">E40</font></i></a>, <a class="ref" href="isocat_1.html#T16" target="_self">Th16</a></i>;<br/>


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