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<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="altcat_1.html#L2" title="ALTCAT_1:struct.2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon" title="c3">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="E1:9"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>
 ;<br/>

<a NAME="E2:9"/><b>then </b><i><font color="Green" title="E5">A2</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="functor0.html#V19" title="FUNCTOR0:attr.19">injective</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></i>;<br/>
<a NAME="E3:9"/><b>then </b>
<font color="Maroon" title="c3">F</font> is <a href="functor0.html#V4" title="FUNCTOR0:attr.4">one-to-one</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D34" title="FUNCTOR0:def.34">FUNCTOR0:def 34</a></i>;<br/>
<a NAME="E4:9"/><b>then </b><i><font color="Green" title="E6">A3</font></i>: 
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D7" title="FUNCTOR0:def.7">FUNCTOR0:def 7</a></i>;<br/>
<a NAME="E5:9"/><i><font color="Green" title="E7">A4</font></i>: 
<font color="Maroon" title="c3">F</font> is <a href="functor0.html#V17" title="FUNCTOR0:attr.17">faithful</a>
 
<b>by </b><i><a class="txt" href="functor1.html#E2:9"><i><font color="Green" title="E5">A2</font></i></a>, <a class="ref" href="functor0.html#D34" title="FUNCTOR0:def.34">FUNCTOR0:def 34</a></i>;<br/>
<a NAME="E6:9"/>
<font color="Maroon" title="c3">F</font> is <a href="functor0.html#V20" title="FUNCTOR0:attr.20">surjective</a>
 
<b>by </b><i><a class="txt" href="functor1.html#E1:9"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="functor0.html#D36" title="FUNCTOR0:def.36">FUNCTOR0:def 36</a></i>;<br/>
<a NAME="E7:9"/><b>then </b>
<font color="Maroon" title="c3">F</font> is <a href="functor0.html#V5" title="FUNCTOR0:attr.5">onto</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D35" title="FUNCTOR0:def.35">FUNCTOR0:def 35</a></i>;<br/>
<a NAME="E8:9"/><b>then </b>
the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> is <a href="funct_2.html#V2" title="FUNCT_2:attr.2">onto</a>
 
<b>by </b><i><a class="ref" href="functor0.html#D8" title="FUNCTOR0:def.8">FUNCTOR0:def 8</a></i>;<br/>
<b>hence </b><a NAME="E9:9"/>
( the <a href="functor0.html#U1" title="FUNCTOR0:sel.1">ObjectMap</a> of <font color="Maroon" title="c3">F</font> is <a href="funct_2.html#V3" title="FUNCT_2:attr.3">bijective</a> &amp; the <a href="functor0.html#U2" title="FUNCTOR0:sel.2">MorphMap</a> of <font color="Maroon" title="c3">F</font> is <a href="msualg_3.html#V1" title="MSUALG_3:attr.1">"1-1"</a> )
 <b>by </b><i><a class="txt" href="functor1.html#E4:9"><i><font color="Green" title="E6">A3</font></i></a>, <a class="txt" href="functor1.html#E5:9"><i><font color="Green" title="E7">A4</font></i></a>, <a class="ref" href="functor0.html#D31" title="FUNCTOR0:def.31">FUNCTOR0:def 31</a>, <a class="ref" href="funct_2.html#D4" title="FUNCT_2:def.4">FUNCT_2:def 4</a></i>;<br/>


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