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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> is <a href="cat_1.html#V8" title="CAT_1:attr.8">isomorphic</a> holds <br/><font color="Olive" title="b1">F</font> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a>  is <a href="cat_1.html#V8" title="CAT_1:attr.8">isomorphic</a></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> is <a href="cat_1.html#V8" title="CAT_1:attr.8">isomorphic</a> implies <font color="Maroon" title="c3">F</font> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a>  is <a href="cat_1.html#V8" title="CAT_1:attr.8">isomorphic</a> )</span><br/>





<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="cat_1.html#V8" title="CAT_1:attr.8">isomorphic</a>
 ; <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#K1" title="ISOCAT_1:func.1">"</a>  is <a href="cat_1.html#V8" title="CAT_1:attr.8">isomorphic</a></span><br/>

<a NAME="E2:12"/><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/>
<a NAME="E3:12"/><i><font color="Green" title="E14">A3</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> 
 
<b>by </b><i><a class="txt" href="#E1:12"><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/>
<b>hence </b><a NAME="E4:12"/>
<font color="Maroon" title="c3">F</font> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</a>  is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 <b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="funct_1.html#T62" title="FUNCT_1:th.62">FUNCT_1:62</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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <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="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font></span><br/>

<b>thus </b> <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <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="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">F</font>
<b>by </b><i><a class="txt" href="#E2:12"><i><font color="Green" title="E13">A2</font></i></a>, <a class="txt" href="#E3:12"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>
<br/>.= 
the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">A</font>
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</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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