<?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> be   <a href="cat_1.html#NM4">Category</a>;<br/>



<b>assume </b><a NAME="E1:73"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="nattra_1.html#V2" target="_self">discrete</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" target="_self">Functors</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="nattra_1.html#D19" target="_self">NATTRA_1:def 19</a><br/>

<a NAME="E2:73"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="cat_1.html#U2">Morphisms</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" target="_self">Functors</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 
;<br/>
<a NAME="E3:73"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="nattra_1.html#K11" target="_self">NatTrans</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="nattra_1.html#D18" target="_self">Def18</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> being    <a href="cat_1.html#M2">Functor</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>6</sub></font> being    <a href="nattra_1.html#M2" target="_self">natural_transformation</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font><b> such that </b><br/><a NAME="E5:73"/><i><font color="Green">E57</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <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>4</sub></font>,<font color="Maroon">c<sub>5</sub></font></span><a href="tarski.html#K4">]</a></span>,<font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K4">]</a></span> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#R2" target="_self">is_naturally_transformable_to</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="nattra_1.html#D16" target="_self">Def16</a></i>;<br/>
<a NAME="E6:73"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="cat_2.html#K7">Funct</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="cat_2.html#D2">CAT_2:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="cat_1.html#NM1">Object</a> of <span class="p1">(<span class="default"><a href="nattra_1.html#K12" target="_self">Functors</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <b>by </b><i><a class="ref" href="nattra_1.html#D18" target="_self">Def18</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>7</sub></font>
;<br/>

<a NAME="E8:73"/>
<font color="Maroon">c<sub>4</sub></font> <a href="nattra_1.html#R1" target="_self">is_transformable_to</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E5:73"><i><font color="Green">E57</font></i></a>, <a class="ref" href="nattra_1.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E9:73"/><b>then </b><i><font color="Green">E58</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="funct_2.html#R2">=</a> <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:73"><i><font color="Green">E56</font></i></a>, <a class="ref" href="nattra_1.html#T49" target="_self">Th49</a></i>;<br/>
<a NAME="E10:73"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#R2">=</a>  <a href="nattra_1.html#K7" target="_self">id</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="nattra_1.html#E1:73"><i><font color="Green">E56</font></i></a>, <a class="ref" href="nattra_1.html#T50" target="_self">Th50</a></i>;<br/>
<b>hence </b><a NAME="E11:73"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="txt" href="nattra_1.html#E5:73"><i><font color="Green">E57</font></i></a>, <a class="txt" href="nattra_1.html#E9:73"><i><font color="Green">E58</font></i></a>, <a class="ref" href="nattra_1.html#D18" target="_self">Def18</a></i>;<br/>


</div>
