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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font>, <font color="Maroon" title="c4">D</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/>







<b>given </b><font color="Maroon" title="c5">F</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><b> such that </b><a NAME="E2:24"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c5">F</font> <a href="isocat_1.html#NR1" title="ISOCAT_1:NR.1">is_an_isomorphism</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D4" target="_self" title="ISOCAT_1:def.4">ISOCAT_1:def 4</a><br/>

<b>given </b><font color="Maroon" title="c6">G</font> being    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c3">C</font>,<font color="Maroon" title="c4">D</font><b> such that </b><a NAME="E4:24"/><i><font color="Green" title="E15">A2</font></i>: 
<font color="Maroon" title="c6">G</font> <a href="isocat_1.html#NR1" title="ISOCAT_1:NR.1">is_an_isomorphism</a> 
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D4" target="_self" title="ISOCAT_1:def.4">ISOCAT_1:def 4</a><br/>

<b>take </b>
<span class="p1"><a href="cat_2.html#K20" title="CAT_2:func.20">[:</a><span class="default"><font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c6">G</font></span><a href="cat_2.html#K20" title="CAT_2:func.20">:]</a></span>
; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D4" target="_self" title="ISOCAT_1:def.4">ISOCAT_1:def 4</a><br/>

<a NAME="E5:24"/>
( <font color="Maroon" title="c5">F</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp; <font color="Maroon" title="c6">G</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> )
 
<b>by </b><i><a class="txt" href="isocat_1.html#E2:24"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="isocat_1.html#E4:24"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="isocat_1.html#D3" target="_self" title="ISOCAT_1:def.3">Def3</a></i>;<br/>
<b>hence </b><a NAME="E6:24"/>
<span class="p1"><a href="cat_2.html#K20" title="CAT_2:func.20">[:</a><span class="default"><font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c6">G</font></span><a href="cat_2.html#K20" title="CAT_2:func.20">:]</a></span> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>by </b><i><a class="ref" href="isocat_1.html#T1" target="_self" title="ISOCAT_1:th.1">Th1</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D3" target="_self" title="ISOCAT_1:def.3">ISOCAT_1:def 3</a><br/>

<b>thus </b> <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="cat_2.html#K20" title="CAT_2:func.20">[:</a><span class="default"><font color="Maroon" title="c5">F</font>,<font color="Maroon" title="c6">G</font></span><a href="cat_2.html#K20" title="CAT_2:func.20">:]</a></span> = 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c5">F</font></span>)</span>,<span class="p2">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">G</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<b>by </b><i><a class="ref" href="funct_3.html#T88" title="FUNCT_3:th.88">FUNCT_3:88</a></i>
<br/>.= 
<span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <font color="Maroon" title="c2">B</font>,<span class="p2">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c6">G</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
<b>by </b><i><a class="txt" href="isocat_1.html#E2:24"><i><font color="Green" title="E14">A1</font></i></a>, <a class="ref" href="isocat_1.html#D3" target="_self" title="ISOCAT_1:def.3">Def3</a></i>
<br/>.= 
the <a href="cat_1.html#U2" title="CAT_1:sel.2">Morphisms</a> of <span class="p1"><a href="cat_2.html#K11" title="CAT_2:func.11">[:</a><span class="default"><font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c4">D</font></span><a href="cat_2.html#K11" title="CAT_2:func.11">:]</a></span>
<b>by </b><i><a class="txt" href="isocat_1.html#E4:24"><i><font color="Green" title="E15">A2</font></i></a>, <a class="ref" href="isocat_1.html#D3" target="_self" title="ISOCAT_1:def.3">Def3</a></i>
;<br/>


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