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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="functor0.html#L2">FunctorStr</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>



<b>assume </b><a NAME="E1:51"/>
( <font color="Maroon">c<sub>3</sub></font> is   <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> is   <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">c<sub>2</sub></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">c<sub>6</sub></font> being  <a href="functor0.html#V16">contravariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font><b> such that </b><a NAME="E2:51"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="functor0.html#V21">bijective</a>
 <b>and </b><br/><a NAME="E3:51"/>
( ( for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font><br/>for <font color="Olive">b<sub>2</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> holds <br/><font color="Maroon">c<sub>6</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font><br/>for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font> st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></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<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>4</sub></font> holds <br/>for <font color="Olive">b<sub>5</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font><br/>for <font color="Olive">b<sub>6</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font> st <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>6</sub></font> holds <br/><font color="Maroon">c<sub>6</sub></font> <a href="functor0.html#K8">.</a> <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K4">Morph-Map</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>6</sub></font> ) )
 ;<br/>

<b>take </b>
<font color="Maroon">c<sub>6</sub></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">c<sub>6</sub></font> is <a href="functor0.html#V21">bijective</a> &amp; <font color="Maroon">c<sub>6</sub></font> is <a href="functor0.html#V16">contravariant</a> )
 <b>by </b><i><a class="txt" href="yellow20.html#E2:51"><i><font color="Green">E32</font></i></a></i>;<br/>


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