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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>;<br/><b>let </b><font color="Maroon" title="c3">F</font> be  <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>;<br/><b>let </b><font color="Maroon" title="c4">o1</font>, <font color="Maroon" title="c5">o2</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font>;<br/><b>let </b><font color="Maroon" title="c6">a</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:35"/><i><font color="Green" title="E22">A1</font></i>: 
( <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V18" title="FUNCTOR0:attr.18">full</a> &amp; <font color="Maroon" title="c3">F</font> is <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a> )
 <b>and </b><br/><a NAME="E2:35"/><i><font color="Green" title="E23">A2</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c4">o1</font>,<font color="Maroon" title="c5">o2</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; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c5">o2</font>,<font color="Maroon" title="c4">o1</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>  )
 <b>and </b><br/><a NAME="E3:35"/><i><font color="Green" title="E24">A3</font></i>: 
<font color="Maroon" title="c3">F</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a>
 ;<br/>

<a NAME="E4:35"/>
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c4">o1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c5">o2</font></span>)</span></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; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c5">o2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c4">o1</font></span>)</span></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>  )
 
<b>by </b><i><a class="txt" href="altcat_4.html#E2:35"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="functor0.html#D20" title="FUNCTOR0:def.20">FUNCTOR0:def 20</a></i>;<br/>
<a NAME="E5:35"/><b>then </b>
( <font color="Maroon" title="c3">F</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V1" title="ALTCAT_3:attr.1">retraction</a> &amp; <font color="Maroon" title="c3">F</font> <a href="functor0.html#K8" title="FUNCTOR0:func.8">.</a> <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> )
 
<b>by </b><i><a class="txt" href="altcat_4.html#E3:35"><i><font color="Green" title="E24">A3</font></i></a>, <a class="ref" href="altcat_3.html#T6" title="ALTCAT_3:th.6">ALTCAT_3:6</a></i>;<br/>
<a NAME="E6:35"/><b>then </b>
( <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V1" title="ALTCAT_3:attr.1">retraction</a> &amp; <font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V2" title="ALTCAT_3:attr.2">coretraction</a> )
 
<b>by </b><i><a class="txt" href="altcat_4.html#E1:35"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="altcat_4.html#E2:35"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="altcat_4.html#T30" target="_self" title="ALTCAT_4:th.30">Th30</a>, <a class="ref" href="altcat_4.html#T31" target="_self" title="ALTCAT_4:th.31">Th31</a></i>;<br/>
<b>hence </b><a NAME="E7:35"/>
<font color="Maroon" title="c6">a</font> is <a href="altcat_3.html#V3" title="ALTCAT_3:attr.3">iso</a>
 <b>by </b><i><a class="txt" href="altcat_4.html#E2:35"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="altcat_3.html#T6" title="ALTCAT_3:th.6">ALTCAT_3:6</a></i>;<br/>


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