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<b>let </b><font color="Maroon" title="c1">C</font>, <font color="Maroon" title="c2">D</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c3">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">C</font>,<font color="Maroon" title="c2">D</font>;<br/><b>let </b><font color="Maroon" title="c4">I</font> be   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c2">D</font>;<br/><b>let </b><font color="Maroon" title="c5">T</font> be    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Maroon" title="c4">I</font>;<br/><b>let </b><font color="Maroon" title="c6">J</font> be   <a href="index_1.html#NM9" title="INDEX_1:NM.9">Indexing</a> of <font color="Maroon" title="c5">T</font>;<br/>









<a NAME="E1:80"/>
<font color="Maroon" title="c4">I</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K15" title="INDEX_1:func.15">-functor</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c5">T</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="index_1.html#K19" title="INDEX_1:func.19">-indexing_of</a> <font color="Maroon" title="c1">C</font>
 
<b>by </b><i><a class="ref" href="index_1.html#T23" target="_self" title="INDEX_1:th.23">Th23</a></i>;<br/>
<a NAME="E2:80"/><b>then </b><i><font color="Green" title="E39">A1</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="index_1.html#K15" title="INDEX_1:func.15">-functor</a> <font color="Maroon" title="c1">C</font>,<span class="p1">(<span class="default"><a href="index_1.html#K16" title="INDEX_1:func.16">rng</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K15" title="INDEX_1:func.15">-functor</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c5">T</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="ref" href="index_1.html#T18" target="_self" title="INDEX_1:th.18">Th18</a></i>;<br/>
<a NAME="E3:80"/><i><font color="Green" title="E40">A2</font></i>: 
 <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K15" title="INDEX_1:func.15">-functor</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c5">T</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c3">F</font></span>)</span> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c5">T</font>
 
;<br/>
<a NAME="E4:80"/>
<font color="Maroon" title="c5">T</font> is    <a href="index_1.html#M4" title="INDEX_1:mode.4">TargetCat</a> of <font color="Maroon" title="c4">I</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c3">F</font>
 
<b>by </b><i><a class="ref" href="index_1.html#T24" target="_self" title="INDEX_1:th.24">Th24</a></i>;<br/>
<a NAME="E5:80"/><b>then </b>
 <a href="index_1.html#K16" title="INDEX_1:func.16">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c3">F</font></span>)</span> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c5">T</font>
 
<b>by </b><i><a class="ref" href="index_1.html#T14" target="_self" title="INDEX_1:th.14">Th14</a></i>;<br/>
<a NAME="E6:80"/><b>then </b><i><font color="Green" title="E41">A3</font></i>: 
 <a href="cat_5.html#K7" title="CAT_5:func.7">Image</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="index_1.html#K15" title="INDEX_1:func.15">-functor</a> <font color="Maroon" title="c1">C</font>,<span class="p2">(<span class="default"><a href="index_1.html#K16" title="INDEX_1:func.16">rng</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c3">F</font></span>)</span></span>)</span></span>)</span> is    <a href="cat_2.html#M3" title="CAT_2:mode.3">Subcategory</a> of <font color="Maroon" title="c5">T</font>
 
<b>by </b><i><a class="ref" href="cat_5.html#T4" title="CAT_5:th.4">CAT_5:4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c6">J</font> <a href="index_1.html#K22" title="INDEX_1:func.22">*</a> <font color="Maroon" title="c4">I</font></span>)</span> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c3">F</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c6">J</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K15" title="INDEX_1:func.15">-functor</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c5">T</font></span>)</span></span>)</span> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c3">F</font>
<b>by </b><i><a class="ref" href="index_1.html#T32" target="_self" title="INDEX_1:th.32">Th32</a></i>
<br/>.= 
<font color="Maroon" title="c6">J</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K15" title="INDEX_1:func.15">-functor</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c5">T</font></span>)</span> <a href="cat_1.html#K14" title="CAT_1:func.14">*</a> <font color="Maroon" title="c3">F</font></span>)</span>
<b>by </b><i><a class="ref" href="index_1.html#T26" target="_self" title="INDEX_1:th.26">Th26</a></i>
<br/>.= 
<font color="Maroon" title="c6">J</font> <a href="index_1.html#K22" title="INDEX_1:func.22">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">I</font> <a href="index_1.html#K20" title="INDEX_1:func.20">*</a> <font color="Maroon" title="c3">F</font></span>)</span>
<b>by </b><i><a class="txt" href="index_1.html#E2:80"><i><font color="Green" title="E39">A1</font></i></a>, <a class="txt" href="index_1.html#E3:80"><i><font color="Green" title="E40">A2</font></i></a>, <a class="txt" href="index_1.html#E6:80"><i><font color="Green" title="E41">A3</font></i></a>, <a class="ref" href="index_1.html#T22" target="_self" title="INDEX_1:th.22">Th22</a></i>
;<br/>


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