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<b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>, <font color="Maroon">D</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">F</font> be    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">C</font>,<font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">I</font> be   <a href="index_1.html#NM9">Indexing</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">T</font> be    <a href="index_1.html#M4" target="_self">TargetCat</a> of <font color="Maroon">I</font>;<br/><b>let </b><font color="Maroon">J</font> be   <a href="index_1.html#NM9">Indexing</a> of <font color="Maroon">T</font>;<br/>









<a NAME="E1:80"/>
<font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">D</font>,<font color="Maroon">T</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font></span>)</span> <a href="index_1.html#K19" target="_self">-indexing_of</a> <font color="Maroon">C</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:80"/><b>then </b><i><font color="Green">E23</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font></span>)</span> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<span class="p1">(<span class="default"><a href="index_1.html#K16" target="_self">rng</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font></span>)</span></span>)</span> <a href="funct_2.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">D</font>,<font color="Maroon">T</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font>
 
<b>by </b><i><a class="txt" href="index_1.html#E3:80"><i><font color="Green">E26</font></i></a></i>;<br/>
<a NAME="E3:80"/><i><font color="Green">E26</font></i>: 
 <a href="cat_5.html#K7">Image</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">D</font>,<font color="Maroon">T</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font></span>)</span> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">T</font>
 
;<br/>
<a NAME="E4:80"/>
<font color="Maroon">T</font> is    <a href="index_1.html#M4" target="_self">TargetCat</a> of <font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font>
 
<b>by </b><i/>;<br/>
<a NAME="E5:80"/><b>then </b>
 <a href="index_1.html#K16" target="_self">rng</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font></span>)</span> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">T</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:80"/><b>then </b><i><font color="Green">E28</font></i>: 
 <a href="cat_5.html#K7">Image</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font></span>)</span> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">C</font>,<span class="p2">(<span class="default"><a href="index_1.html#K16" target="_self">rng</a> <span class="p3">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font></span>)</span></span>)</span></span>)</span> is    <a href="cat_2.html#M3">Subcategory</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="cat_5.html#T4">CAT_5:4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="index_1.html#K22" target="_self">*</a> <font color="Maroon">I</font></span>)</span> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font> = 
<span class="p1">(<span class="default"><font color="Maroon">J</font> <a href="index_1.html#K20" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">D</font>,<font color="Maroon">T</font></span>)</span></span>)</span> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">J</font> <a href="index_1.html#K20" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K15" target="_self">-functor</a> <font color="Maroon">D</font>,<font color="Maroon">T</font></span>)</span> <a href="cat_1.html#K14">*</a> <font color="Maroon">F</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">J</font> <a href="index_1.html#K22" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">I</font> <a href="index_1.html#K20" target="_self">*</a> <font color="Maroon">F</font></span>)</span>
<b>by </b><i>, , , <a class="ref" href="index_1.html#T2" target="_self">Th2</a></i>
;<br/>


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