<?xml version="1.0"?>
<div>:: <span class="kw">deftheorem </span>   defines <a href="cat_7.html#V9" title="CAT_7:attr.9">isomorphism</a> <a onclick="hs(this)" href="javascript:()">CAT_7:def 19 : <br/></a><span> for <font color="Olive" title="b1">C</font>, <font color="Olive" title="b2">D</font> being   <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><br/>  for <font color="Olive" title="b3">F</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">C</font>,<font color="Olive" title="b2">D</font> holds <br/> ( <font color="Olive" title="b3">F</font> is  <a href="cat_7.html#V9" title="CAT_7:attr.9">isomorphism</a>  iff ( <font color="Olive" title="b3">F</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp;  ex <font color="Olive" title="b4">G</font> being   <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b2">D</font>,<font color="Olive" title="b1">C</font> st <br/>( <font color="Olive" title="b4">G</font> is  <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  &amp; <font color="Olive" title="b4">G</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b3">F</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Olive" title="b1">C</font> &amp; <font color="Olive" title="b3">F</font> <a href="cat_6.html#K11" title="CAT_6:func.11">(*)</a> <font color="Olive" title="b4">G</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="cat_6.html#K12" title="CAT_6:func.12">id</a> <font color="Olive" title="b2">D</font> ) ) );<br/></span></div>
