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

<b>let </b><font color="Maroon" title="c1">A</font>, <font color="Maroon" title="c2">B</font> be   <a href="cat_1.html#NM4" title="CAT_1:NM.4">Category</a>;<br/><b>let </b><font color="Maroon" title="c3">F1</font>, <font color="Maroon" title="c4">F2</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>;<br/>





<b>assume </b><a NAME="E1:15"/><i><font color="Green" title="E12">A1</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being  <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">A</font>  st  <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  holds <br/>for <font color="Olive" title="b3">f</font> being   <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> holds  <font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Olive" title="b3">f</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">f</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c1">A</font>;<br/><b>reconsider </b><font color="Maroon" title="c6">f'</font> = <font color="Maroon" title="c5">f</font> as    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of  <a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">f</font>, <a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c5">f</font> <b>by </b><i><a class="ref" href="cat_1.html#T22" title="CAT_1:th.22">CAT_1:22</a></i>;<br/><a NAME="E2:15_1"/><i><font color="Green" title="E13">A2</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <span class="p1">(<span class="default"><a href="cat_1.html#K3" title="CAT_1:func.3">dom</a> <font color="Maroon" title="c5">f</font></span>)</span>,<span class="p1">(<span class="default"><a href="cat_1.html#K4" title="CAT_1:func.4">cod</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 <b>by </b><i><a class="ref" href="cat_1.html#T19" title="CAT_1:th.19">CAT_1:19</a></i>;<br/><b>hence </b><font color="Maroon" title="c3">F1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">f</font> = 
<font color="Maroon" title="c3">F1</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f'</font>
<b>by </b><i><a class="ref" href="nattra_1.html#D1" target="_self" title="NATTRA_1:def.1">Def1</a></i>
<br/>.= 
<font color="Maroon" title="c4">F2</font> <a href="nattra_1.html#K3" title="NATTRA_1:func.3">.</a> <font color="Maroon" title="c6">f'</font>
<b>by </b><i><a class="txt" href="nattra_1.html#E1:15"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="nattra_1.html#E2:15_1"><i><font color="Green" title="E13">A2</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c4">F2</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">f</font>
<b>by </b><i><a class="txt" href="nattra_1.html#E2:15_1"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="nattra_1.html#D1" target="_self" title="NATTRA_1:def.1">Def1</a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:15"/>
<font color="Maroon" title="c3">F1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">F2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>


</div>
