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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> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c4">F</font> be    <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>;<br/><b>let </b><font color="Maroon" title="c5">G</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:17"/><i><font color="Green" title="E14">A1</font></i>: 
<font color="Maroon" title="c4">F</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green" title="E15">A2</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c2">B</font>
 <b>and </b><br/><a NAME="E3:17"/><i><font color="Green" title="E16">A3</font></i>: 
<font color="Maroon" title="c5">G</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>and </b><br/><a NAME="E4:17"/><i><font color="Green" title="E17">A4</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c5">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c3">C</font>
 ; <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 NAME="E5:17"/>
<font color="Maroon" title="c5">G</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</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#E1:17"><i><font color="Green" title="E14">A1</font></i></a>, <a class="txt" href="isocat_1.html#E3:17"><i><font color="Green" title="E16">A3</font></i></a>, <a class="ref" href="funct_1.html#T46" title="FUNCT_1:th.46">FUNCT_1:46</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/>

<a NAME="E6:17"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c2">B</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E7:17"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c3">C</font>
 <b>by </b><i><a class="txt" href="isocat_1.html#E2:17"><i><font color="Green" title="E15">A2</font></i></a>, <a class="txt" href="isocat_1.html#E4:17"><i><font color="Green" title="E17">A4</font></i></a>, <a class="ref" href="relat_1.html#T47" title="RELAT_1:th.47">RELAT_1:47</a></i>;<br/>


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