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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">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>  st <font color="Olive" title="b1">F</font> <a href="isocat_1.html#NR1" title="ISOCAT_1:NR.1">is_an_isomorphism</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">F</font> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a> </span>)</span> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">F</font></span><br/><b>let </b><font color="Maroon" title="c3">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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">F</font> <a href="isocat_1.html#NR1" title="ISOCAT_1:NR.1">is_an_isomorphism</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a> </span>)</span> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">F</font> )</span><br/>





<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="isocat_1.html#NR1" title="ISOCAT_1:NR.1">is_an_isomorphism</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a> </span>)</span> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c3">F</font></span><br/>

<a NAME="E2:15"/><b>then </b><i><font color="Green" title="E13">A2</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="cat_1.html#D22" title="CAT_1:def.22">CAT_1:def 22</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c4">f</font> = <font color="Maroon" title="c3">F</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">A</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c2">B</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c5">g</font> = <font color="Maroon" title="c3">F</font> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a>  as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c2">B</font>,the <a href="graph_1.html#U2" title="GRAPH_1:sel.2">Edges</a> of <font color="Maroon" title="c1">A</font> ;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a> </span>)</span> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a>  = 
<font color="Maroon" title="c5">g</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="isocat_1.html#D2" target="_self" title="ISOCAT_1:def.2">Def2</a>, <a class="ref" href="isocat_1.html#T13" target="_self" title="ISOCAT_1:th.13">Th13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
<b>by </b><i><a class="txt" href="isocat_1.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="isocat_1.html#D2" target="_self" title="ISOCAT_1:def.2">Def2</a></i>
<br/>.= 
<font color="Maroon" title="c3">F</font>
<b>by </b><i><a class="txt" href="isocat_1.html#E2:15"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="funct_1.html#T65" title="FUNCT_1:th.65">FUNCT_1:65</a></i>
; <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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