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<b>let </b><font color="Maroon">A</font> be   <a href="altcat_1.html#NM4">category</a>, <font color="Maroon">B</font> be   <a href="altcat_1.html#NM4">category</a>, <font color="Maroon">A'</font> be   <a href="altcat_1.html#NM4">category</a>, <font color="Maroon">B'</font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="functor0.html#L2">FunctorStr</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/>



<b>assume </b><a NAME="E1:51"/>
( <font color="Maroon">A'</font> is   <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">A</font> &amp; <font color="Maroon">B'</font> is   <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">B</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow20.html#D5" target="_self">YELLOW20:def 5</a><br/>

<b>given </b><font color="Maroon">G</font> being  <a href="functor0.html#V16">contravariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">A'</font>,<font color="Maroon">B'</font><b> such that </b><a NAME="E2:51"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">G</font> is <a href="functor0.html#V21">bijective</a>
 <b>and </b><br/><a NAME="E3:51"/>
( ( for <font color="Olive">a'</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A'</font><br/> for <font color="Olive">a</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>  st <font color="Olive">a'</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> holds <br/><font color="Maroon">G</font> <a href="functor0.html#K3">.</a> <font color="Olive">a'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F</font> <a href="functor0.html#K3">.</a> <font color="Olive">a</font> ) &amp; ( for <font color="Olive">b'</font>, <font color="Olive">c'</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A'</font><br/> for <font color="Olive">b</font>, <font color="Olive">c</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>  st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b'</font>,<font color="Olive">c'</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">b'</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> &amp; <font color="Olive">c'</font> <a href="hidden.html#R1">=</a> <font color="Olive">c</font> holds <br/>for <font color="Olive">f'</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b'</font>,<font color="Olive">c'</font><br/> for <font color="Olive">f</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b</font>,<font color="Olive">c</font>  st <font color="Olive">f'</font> <a href="hidden.html#R1">=</a> <font color="Olive">f</font> holds <br/><font color="Maroon">G</font> <a href="functor0.html#K8">.</a> <font color="Olive">f'</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4">Morph-Map</a> <font color="Maroon">F</font>,<font color="Olive">b</font>,<font color="Olive">c</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">f</font> ) )
 ;<br/>

<b>take </b>
<font color="Maroon">G</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D41">FUNCTOR0:def 41</a><br/>

<b>thus </b><a NAME="E4:51"/>
( <font color="Maroon">G</font> is <a href="functor0.html#V21">bijective</a> &amp; <font color="Maroon">G</font> is <a href="functor0.html#V16">contravariant</a> )
 <b>by </b><i/>;<br/>


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