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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#V15" title="FUNCTOR0:attr.15">covariant</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>assume </b><a NAME="E1:8"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>
 ;<br/>

<b>let </b><font color="Maroon" title="c4">G</font> be  <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="c2">B</font>,<font color="Maroon" title="c1">A</font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E2:8"/><i><font color="Green" title="E7">A2</font></i>: 
for <font color="Olive" title="b1">b</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c4">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">b</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">b</font>
 <b>and </b><br/><a NAME="E3:8"/><i><font color="Green" title="E8">A3</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</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">a</font>,<font color="Olive" title="b2">b</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>  holds <br/>for <font color="Olive" title="b3">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <font color="Maroon" title="c4">G</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">f</font>
 ;<br/>

<div><i><font color="Green" title="E9">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">b</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>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c5">b</font> = 
<font color="Maroon" title="c4">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<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">b</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#T34" title="FUNCTOR0:th.34">FUNCTOR0:34</a></i>
<br/>.= 
<font color="Maroon" title="c5">b</font>
<b>by </b><i><a class="txt" href="yellow20.html#E2:8"><i><font color="Green" title="E7">A2</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K12" title="FUNCTOR0:func.12">id</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c5">b</font>
<b>by </b><i><a class="ref" href="functor0.html#T30" title="FUNCTOR0:th.30">FUNCTOR0:30</a></i>
;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</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>assume </b><a NAME="E1:8_2"/><i><font color="Green" title="E10">A5</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="c5">a</font>,<font color="Maroon" title="c6">b</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> 
 ;<br/><b>let </b><font color="Maroon" title="c7">f</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c5">a</font>,<font color="Maroon" title="c6">b</font>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c4">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c7">f</font> = 
<font color="Maroon" title="c4">G</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c7">f</font></span>)</span>
<b>by </b><i><a class="txt" href="yellow20.html#E1:8_2"><i><font color="Green" title="E10">A5</font></i></a>, <a class="ref" href="functor3.html#T6" title="FUNCTOR3:th.6">FUNCTOR3:6</a></i>
<br/>.= 
<font color="Maroon" title="c7">f</font>
<b>by </b><i><a class="txt" href="yellow20.html#E3:8"><i><font color="Green" title="E8">A3</font></i></a>, <a class="txt" href="yellow20.html#E1:8_2"><i><font color="Green" title="E10">A5</font></i></a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K12" title="FUNCTOR0:func.12">id</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c7">f</font>
<b>by </b><i><a class="txt" href="yellow20.html#E1:8_2"><i><font color="Green" title="E10">A5</font></i></a>, <a class="ref" href="functor0.html#T32" title="FUNCTOR0:th.32">FUNCTOR0:32</a></i>
;<br/></div><b>end;</b></div>
<a NAME="E6:8"/><b>then </b>
<font color="Maroon" title="c4">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="functor0.html#K12" title="FUNCTOR0:func.12">id</a> <font color="Maroon" title="c1">A</font>
 
<b>by </b><i><a class="txt" href="yellow20.html#E4:8"><i><font color="Green" title="E9">A4</font></i></a>, <a class="ref" href="yellow18.html#T1" title="YELLOW18:th.1">YELLOW18:1</a></i>;<br/>
<b>hence </b><a NAME="E7:8"/>
 <a href="functor0.html#G2" title="FUNCTOR0:aggr.2">FunctorStr</a>(# the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c4">G</font>,the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c4">G</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F</font> <a href="functor0.html#K15" title="FUNCTOR0:func.15">"</a> 
 <b>by </b><i><a class="txt" href="yellow20.html#E1:8"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="yellow20.html#T5" target="_self" title="YELLOW20:th.5">Th5</a></i>;<br/>


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