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<b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">A</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/>





<b>assume </b><a NAME="E1:7"/>
<font color="Maroon">F</font> <a href="cat_1.html#NR2" target="_self">is_an_isomorphism</a> 
 ;<br/>

<a NAME="E2:7"/><b>then </b><i><font color="Green">E18</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">B</font>
 
<b>by </b><i><a class="ref" href="cat_1.html#D22">CAT_1:def 22</a></i>;<br/>
<b>let </b><font color="Maroon">g</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">B</font>;<br/>

<b>consider </b><font color="Maroon">f</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E4:7"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">F</font> &amp; <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> )
 <b>by </b><i>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">f</font> = <font color="Maroon">f</font> as   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">A</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E6:7"/>
<font color="Maroon">F</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font>
 <b>by </b><i/>;<br/>


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