<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="cat_1.html#M2">Functor</a> of <span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="cat_2.html#K11">:]</a></span>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<a NAME="E1:33"/>
the <a href="cat_1.html#U1">Objects</a> of <span class="p1"><a href="cat_2.html#K11">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="cat_2.html#K11">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="cat_2.html#T33">CAT_2:33</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> =  <a href="nattra_1.html#K7">id</a> <font color="Maroon">c<sub>4</sub></font> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="cat_1.html#U1">Objects</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>,the <a href="cat_1.html#U2">Morphisms</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>6</sub></font> as    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="ref" href="isocat_2.html#T8" target="_self">Th8</a></i>;<br/><div><i><font color="Green">E30</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><a NAME="E1:33_1_1"/><i><font color="Green">E31</font></i>: 
 <a href="cat_1.html#K6">Hom</a> <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="cat_1.html#T56">CAT_1:56</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><a href="nattra_1.html#K7">id</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font> = 
<span class="p1">(<span class="default"><a href="nattra_1.html#K7">id</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="nattra_1.html#T21">NATTRA_1:21</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T108">CAT_1:108</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font> <a href="nattra_1.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:33_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="nattra_1.html#D1">NATTRA_1:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="nattra_1.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="isocat_2.html#T24" target="_self">Th24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cat_2.html#K15">?-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="isocat_2.html#E1:33_1_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="nattra_1.html#D1">NATTRA_1:def 1</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="cat_2.html#K14">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T47">CAT_2:47</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="cat_1.html#K10">id</a> <span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="cat_2.html#K12">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="cat_2.html#T41">CAT_2:41</a></i>
<br/>.= 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="cat_1.html#K13">.</a> <span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="cat_2.html#K12">]</a></span></span>)</span>
<b>by </b><i><a class="ref" href="cat_1.html#T108">CAT_1:108</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="nattra_1.html#K7">id</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="nattra_1.html#K5">.</a> <span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="cat_2.html#K12">]</a></span>
<b>by </b><i><a class="ref" href="nattra_1.html#T21">NATTRA_1:21</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="nattra_1.html#K7">id</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="nattra_1.html#D5">NATTRA_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="cat_2.html#K2">curry</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="cat_2.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>8</sub></font>
<b>by </b><i><a class="ref" href="cat_2.html#T3">CAT_2:3</a></i>
;<br/></div><b>end;</b></div><b>thus </b><span class="p1">(<span class="default"><a href="nattra_1.html#K7">id</a> <span class="p2">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="nattra_1.html#T21">NATTRA_1:21</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="tarski.html#K4">]</a></span>,<span class="p2">(<span class="default"><a href="nattra_1.html#K7">id</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="ref" href="nattra_1.html#D18">NATTRA_1:def 18</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2"><a href="cat_2.html#K12">[</a><span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K13">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="cat_2.html#K12">]</a></span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_2.html#K2">curry</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="cat_2.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="tarski.html#K4">]</a></span>
<b>by </b><i><a class="txt" href="isocat_2.html#E2:33_1"><i><font color="Green">E30</font></i></a>, <a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="isocat_2.html#K6" target="_self">export</a> <span class="p2">(<span class="default"><a href="nattra_1.html#K7">id</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="nattra_1.html#K5">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="ref" href="isocat_2.html#D5" target="_self">Def5</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:33"/>
 <a href="nattra_1.html#K7">id</a> <span class="p1">(<span class="default"><a href="isocat_2.html#K5" target="_self">export</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="isocat_2.html#K6" target="_self">export</a> <span class="p1">(<span class="default"><a href="nattra_1.html#K7">id</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="nattra_1.html#T20">NATTRA_1:20</a></i>;<br/>


</div>
