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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"> ( <font color="Maroon" title="c1">A</font> <a href="isocat_1.html#NR3" title="ISOCAT_1:NR.3">~=</a> <font color="Maroon" title="c2">B</font> implies <font color="Maroon" title="c1">A</font> <a href="isocat_1.html#R2" title="ISOCAT_1:pred.2">is_equivalent_with</a> <font color="Maroon" title="c2">B</font> )</span><br/>



<b>given </b><font color="Maroon" title="c3">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="E2:57"/><i><font color="Green" title="E38">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> 
 ; <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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">A</font> <a href="isocat_1.html#R2" title="ISOCAT_1:pred.2">is_equivalent_with</a> <font color="Maroon" title="c2">B</font></span><br/>

<b>take </b>
<font color="Maroon" title="c3">F</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="isocat_1.html#D10" target="_self" title="ISOCAT_1:def.10">ISOCAT_1:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">G</font> being   <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="c1">A</font> st <br/>( <font color="Olive" title="b1">G</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c3">F</font> <a href="nattra_1.html#NR4" title="NATTRA_1:NR.4">~=</a>  <a href="cat_1.html#K15" title="CAT_1:func.15">id</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Olive" title="b1">G</font> <a href="nattra_1.html#NR4" title="NATTRA_1:NR.4">~=</a>  <a href="cat_1.html#K15" title="CAT_1:func.15">id</a> <font color="Maroon" title="c2">B</font> )</span><br/>

<b>take </b>
<font color="Maroon" title="c3">F</font> <a href="isocat_1.html#K1" title="ISOCAT_1:func.1">"</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="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c3">F</font> <a href="nattra_1.html#NR4" title="NATTRA_1:NR.4">~=</a>  <a href="cat_1.html#K15" title="CAT_1:func.15">id</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</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="nattra_1.html#NR4" title="NATTRA_1:NR.4">~=</a>  <a href="cat_1.html#K15" title="CAT_1:func.15">id</a> <font color="Maroon" title="c2">B</font> )</span><br/>

<b>thus </b><a NAME="E3:57"/>
( <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="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c3">F</font> <a href="nattra_1.html#NR4" title="NATTRA_1:NR.4">~=</a>  <a href="cat_1.html#K15" title="CAT_1:func.15">id</a> <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c3">F</font> <a href="cat_1.html#K14" title="CAT_1:func.14">*</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="nattra_1.html#NR4" title="NATTRA_1:NR.4">~=</a>  <a href="cat_1.html#K15" title="CAT_1:func.15">id</a> <font color="Maroon" title="c2">B</font> )
 <b>by </b><i><a class="txt" href="isocat_1.html#E2:57"><i><font color="Green" title="E38">A1</font></i></a>, <a class="ref" href="isocat_1.html#T16" target="_self" title="ISOCAT_1:th.16">Th16</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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