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<b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">C</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">D</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">T</font> be    <a href="cat_1.html#M2" target="_self">Functor</a> of <font color="Maroon">B</font>,<font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">S</font> be    <a href="cat_1.html#M2" target="_self">Functor</a> of <font color="Maroon">C</font>,<font color="Maroon">D</font>;<br/>









<b>assume </b><b>that </b><br/><a NAME="E1:106"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">T</font> is <a href="cat_1.html#V10" target="_self">faithful</a>
 <b>and </b><br/><a NAME="E2:106"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">S</font> is <a href="cat_1.html#V10" target="_self">faithful</a>
 ;<br/>

<b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>, <font color="Maroon">b'</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_1.html#D24" target="_self">CAT_1:def 24</a><br/>

<b>assume </b><a NAME="E3:106"/><i><font color="Green">E22</font></i>: 
 <a href="cat_1.html#K6" target="_self">Hom</a> <font color="Maroon">b</font>,<font color="Maroon">b'</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>let </b><font color="Maroon">f1</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">b</font>,<font color="Maroon">b'</font>, <font color="Maroon">f2</font> be    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">b</font>,<font color="Maroon">b'</font>;<br/>

<b>assume </b><a NAME="E4:106"/><i><font color="Green">E23</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">T</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">T</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font>
 ;<br/>

<a NAME="E5:106"/>
(  <a href="cat_1.html#K6" target="_self">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">b'</font></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">T</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon">S</font> <a href="cat_1.html#K14" target="_self">*</a> <font color="Maroon">T</font></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">S</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font></span>)</span> &amp; <font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font> is    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">T</font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">b</font>,<font color="Maroon">T</font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">b'</font> &amp; <font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font> is    <a href="cat_1.html#M1" target="_self">Morphism</a> of <font color="Maroon">T</font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">b</font>,<font color="Maroon">T</font> <a href="cat_1.html#K13" target="_self">.</a> <font color="Maroon">b'</font> )
 
<b>by </b><i><a class="ref" href="cat_1.html#T43" target="_self">Th43</a>, , <a class="ref" href="cat_1.html#T40" target="_self">Th40</a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>
<a NAME="E6:106"/><b>then </b>
<font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">T</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">f2</font>
 
<b>by </b><i><a class="ref" href="cat_1.html#T42" target="_self">Th42</a>, <a class="ref" href="cat_1.html#T44" target="_self">Th44</a>, </i>;<br/>
<b>hence </b><a NAME="E7:106"/>
<font color="Maroon">f1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f2</font>
 <b>by </b><i><a class="ref" href="cat_1.html#T41" target="_self">Th41</a>, <a class="ref" href="cat_1.html#T43" target="_self">Th43</a>, </i>;<br/>


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