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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">A'</font>, <font color="Maroon" title="c4">B'</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>;<br/><b>let </b><font color="Maroon" title="c5">F</font> be    <a href="functor0.html#L2" title="FUNCTOR0:struct.2">FunctorStr</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>;<br/>



<b>assume </b><a NAME="E1:50"/>
( <font color="Maroon" title="c3">A'</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A</font> &amp; <font color="Maroon" title="c4">B'</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">B</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow20.html#D4" target="_self" title="YELLOW20:def.4">YELLOW20:def 4</a><br/>

<b>given </b><font color="Maroon" title="c6">G</font> being  <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c3">A'</font>,<font color="Maroon" title="c4">B'</font><b> such that </b><a NAME="E2:50"/><i><font color="Green" title="E32">A1</font></i>: 
<font color="Maroon" title="c6">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>
 <b>and </b><br/><a NAME="E3:50"/>
( ( for <font color="Olive" title="b1">a'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c3">A'</font><br/> for <font color="Olive" title="b2">a</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font>  st <font color="Olive" title="b1">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a</font> holds <br/><font color="Maroon" title="c6">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">a'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b2">a</font> ) &amp; ( for <font color="Olive" title="b1">b'</font>, <font color="Olive" title="b2">c'</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c3">A'</font><br/> for <font color="Olive" title="b3">b</font>, <font color="Olive" title="b4">c</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">b'</font>,<font color="Olive" title="b2">c'</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">b'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b</font> &amp; <font color="Olive" title="b2">c'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">c</font> holds <br/>for <font color="Olive" title="b5">f'</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b'</font>,<font color="Olive" title="b2">c'</font><br/> for <font color="Olive" title="b6">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font>  st <font color="Olive" title="b5">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">f</font> holds <br/><font color="Maroon" title="c6">G</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Olive" title="b5">f'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" title="FUNCTOR0:func.4">Morph-Map</a> <font color="Maroon" title="c5">F</font>,<font color="Olive" title="b3">b</font>,<font color="Olive" title="b4">c</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">f</font> ) )
 ;<br/>

<b>take </b>
<font color="Maroon" title="c6">G</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D40" title="FUNCTOR0:def.40">FUNCTOR0:def 40</a><br/>

<b>thus </b><a NAME="E4:50"/>
( <font color="Maroon" title="c6">G</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a> &amp; <font color="Maroon" title="c6">G</font> is <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a> )
 <b>by </b><i><a class="txt" href="yellow20.html#E2:50"><i><font color="Green" title="E32">A1</font></i></a></i>;<br/>


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