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<span class="kw">let </span><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font>, <font color="Maroon" title="c3">C</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">F</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font><br/> for <font color="Olive" title="b2">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font> holds  <font color="Olive" title="b2">G</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <font color="Olive" title="b1">F</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">G</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Olive" title="b1">F</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">G</font> being   <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font> holds  <font color="Olive" title="b1">G</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">G</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">G</font> be    <a href="cat_1.html#M2" title="CAT_1:mode.2">Functor</a> of <font color="Maroon" title="c2">B</font>,<font color="Maroon" title="c3">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c5">G</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F</font></span>)</span></span><br/>









<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c6">a</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font></span><br/><span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <span class="p2">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font> = 
<font color="Maroon" title="c5">G</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_1.html#T28" target="_self" title="ISOCAT_1:th.28">Th28</a></span>
<br/>.= 
<font color="Maroon" title="c5">G</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T21" title="NATTRA_1:th.21">NATTRA_1:21</a></span>
<br/>.= 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T15" title="NATTRA_1:th.15">NATTRA_1:15</a></span>
<br/>.= 
 <a href="cat_1.html#K6" title="CAT_1:func.6">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">.</a> <font color="Maroon" title="c6">a</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="cat_1.html#T113" title="CAT_1:th.113">CAT_1:113</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F</font></span>)</span></span>)</span> <a href="nattra_1.html#K5" title="NATTRA_1:func.5">.</a> <font color="Maroon" title="c6">a</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="nattra_1.html#T21" title="NATTRA_1:th.21">NATTRA_1:21</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:46"/>
<font color="Maroon" title="c5">G</font> <a href="isocat_1.html#K4" title="ISOCAT_1:func.4">*</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="nattra_1.html#K7" title="NATTRA_1:func.7">id</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="cat_1.html#K10" title="CAT_1:func.10">*</a> <font color="Maroon" title="c4">F</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="isocat_1.html#T31" target="_self" title="ISOCAT_1:th.31">Th31</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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