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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="cat_4.html#NM1">Cartesian_category</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="cat_1.html#NM1">Object</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>thus </b><a NAME="E1:53"/>
(  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="cat_1.html#K6">Hom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <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_4.html#T38" target="_self">Th38</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="cat_4.html#D2" target="_self">CAT_4:def 2</a><br/>

<b>take </b>
 <a href="cat_4.html#K16" target="_self">Alpha</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>take </b>
 <a href="cat_4.html#K17" target="_self">Alpha'</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>thus </b><a NAME="E2:53"/>
( <span class="p1">(<span class="default"><a href="cat_4.html#K16" target="_self">Alpha</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K17" target="_self">Alpha'</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> &amp; <span class="p1">(<span class="default"><a href="cat_4.html#K17" target="_self">Alpha'</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="cat_1.html#K9">*</a> <span class="p1">(<span class="default"><a href="cat_4.html#K16" target="_self">Alpha</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="cat_1.html#K10">id</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="cat_4.html#K2" target="_self">[x]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="cat_4.html#T39" target="_self">Th39</a></i>;<br/>


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