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<b>let </b><font color="Maroon">A</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">B</font> be   <a href="cat_1.html#NM4">Category</a>;<br/><b>let </b><font color="Maroon">a1</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>, <font color="Maroon">a2</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>, <font color="Maroon">b2</font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">A</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="cat_1.html#NM2">Morphism</a> of <font color="Maroon">B</font>;<br/>











<b>assume </b><a NAME="E1:19"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">a1</font>,<font color="Maroon">a2</font> &amp; <font color="Maroon">g</font> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font> )
 ;<br/>

<a NAME="E2:19"/><b>then </b>
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="cat_1.html#K6">Hom</a> <font color="Maroon">a1</font>,<font color="Maroon">a2</font></span>)</span>,<span class="p2">(<span class="default"><a href="cat_1.html#K6">Hom</a> <font color="Maroon">b1</font>,<font color="Maroon">b2</font></span>)</span></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>hence </b><a NAME="E3:19"/>
<span class="p1"><a href="cat_2.html#K13">[</a><span class="default"><font color="Maroon">f</font>,<font color="Maroon">g</font></span><a href="cat_2.html#K13">]</a></span> <a href="hidden.html#R2">in</a>  <a href="cat_1.html#K6">Hom</a> <span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">b1</font></span><a href="cat_2.html#K12">]</a></span>,<span class="p1"><a href="cat_2.html#K12">[</a><span class="default"><font color="Maroon">a2</font>,<font color="Maroon">b2</font></span><a href="cat_2.html#K12">]</a></span>
 <b>by </b><i><a class="ref" href="cat_2.html#T42">CAT_2:42</a></i>;<br/>


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