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<a NAME="E1:37_1_1"/>
the <a href="graph_1.html#U1" title="GRAPH_1:sel.1">Vertices</a> of <font color="Maroon" title="c1">C</font> is <a href="cat_5.html#V2" title="CAT_5:attr.2">categorial</a>
 
<b>by </b><i><a class="ref" href="cat_5.html#D6" target="_self" title="CAT_5:def.6">Def6</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">A</font> =  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c4">B</font> =  <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">m</font> as   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a> <b>by </b><i><a class="ref" href="cat_5.html#D4" target="_self" title="CAT_5:def.4">Def4</a></i>;<br/>
<b>consider </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="c3">A</font>,<font color="Maroon" title="c4">B</font><b> such that </b><br/><a NAME="E4:37_1_1"/><i><font color="Green" title="E23">A1</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">A</font>,<font color="Maroon" title="c4">B</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Maroon" title="c5">F</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <b>by </b><i><a class="ref" href="cat_5.html#D6" target="_self" title="CAT_5:def.6">Def6</a></i>;<br/>
<a NAME="E5:37_1_1"/>
( <font color="Maroon" title="c2">m</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> &amp;  <a href="cat_5.html#K10" title="CAT_5:func.10">cat</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> &amp;  <a href="cat_5.html#K10" title="CAT_5:func.10">cat</a> <font color="Maroon" title="c4">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> )
 
<b>by </b><i><a class="txt" href="cat_5.html#E4:37_1_1"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="cat_5.html#D7" target="_self" title="CAT_5:def.7">Def7</a>, <a class="ref" href="mcart_1.html#T7" title="MCART_1:th.7">MCART_1:7</a></i>;<br/>
<b>hence </b><a NAME="E6:37_1_1"/>
<font color="Maroon" title="c2">m</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  is    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of  <a href="cat_5.html#K10" title="CAT_5:func.10">cat</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c2">m</font></span>)</span>, <a href="cat_5.html#K10" title="CAT_5:func.10">cat</a> <span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c2">m</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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