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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="altcat_1.html#NM4">category</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="functor0.html#V16">contravariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:36"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V18">full</a> &amp; <font color="Maroon">c<sub>3</sub></font> is <a href="functor0.html#V17">faithful</a> )
 <b>and </b><br/><a NAME="E2:36"/><i><font color="Green">E23</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</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; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</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>  )
 <b>and </b><br/><a NAME="E3:36"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="altcat_3.html#R2">are_iso</a> 
 ;<br/>

<b>thus </b><a NAME="E4:36"/>
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</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; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>4</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>  )
 <b>by </b><i><a class="txt" href="altcat_4.html#E2:36"><i><font color="Green">E23</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="altcat_3.html#D6">ALTCAT_3:def 6</a><br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="altcat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K3">.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span><b> such that </b><br/><a NAME="E6:36"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="altcat_3.html#V3">iso</a>
 <b>by </b><i><a class="txt" href="altcat_4.html#E3:36"><i><font color="Green">E24</font></i></a>, <a class="ref" href="altcat_3.html#D6">ALTCAT_3:def 6</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E8:36"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="functor0.html#K8">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="altcat_4.html#E1:36"><i><font color="Green">E22</font></i></a>, <a class="txt" href="altcat_4.html#E2:36"><i><font color="Green">E23</font></i></a>, <a class="ref" href="altcat_4.html#T17" target="_self">Th17</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<b>thus </b><a NAME="E9:36"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="altcat_3.html#V3">iso</a>
 <b>by </b><i><a class="txt" href="altcat_4.html#E1:36"><i><font color="Green">E22</font></i></a>, <a class="txt" href="altcat_4.html#E2:36"><i><font color="Green">E23</font></i></a>, <a class="txt" href="altcat_4.html#E6:36"><i><font color="Green">E25</font></i></a>, <a class="txt" href="altcat_4.html#E8:36"><i><font color="Green">E26</font></i></a>, <a class="ref" href="altcat_4.html#T32" target="_self">Th32</a></i>;<br/>


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