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<b>let </b><font color="Maroon" title="c1">C</font> be   <a href="cat_4.html#NM2" title="CAT_4:NM.2">Cocartesian_category</a>;<br/><b>let </b><font color="Maroon" title="c2">a</font>, <font color="Maroon" title="c3">c</font>, <font color="Maroon" title="c4">b</font> be   <a href="cat_1.html#NM1" title="CAT_1:NM.1">Object</a> of <font color="Maroon" title="c1">C</font>;<br/><b>let </b><font color="Maroon" title="c5">f</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">c</font>;<br/><b>let </b><font color="Maroon" title="c6">g</font> be    <a href="cat_1.html#M1" title="CAT_1:mode.1">Morphism</a> of <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:109"/><i><font color="Green" title="E49">A1</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c3">c</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> 
 <b>and </b><br/><a NAME="E2:109"/><i><font color="Green" title="E50">A2</font></i>: 
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c3">c</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> 
 ;<br/>

<a NAME="E3:109"/>
 <a href="cat_1.html#K7" title="CAT_1:func.7">Hom</a> <font color="Maroon" title="c3">c</font>,<font color="Maroon" title="c3">c</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> 
 
<b>by </b><i><a class="ref" href="cat_1.html#T56" title="CAT_1:th.56">CAT_1:56</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="cat_4.html#K28" title="CAT_4:func.28">nabla</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">f</font> <a href="cat_4.html#K29" title="CAT_4:func.29">+</a> <font color="Maroon" title="c6">g</font></span>)</span> = 
<span class="p1"><a href="cat_4.html#K27" title="CAT_4:func.27">[$</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c5">f</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c6">g</font></span>)</span></span><a href="cat_4.html#K27" title="CAT_4:func.27">$]</a></span>
<b>by </b><i><a class="txt" href="cat_4.html#E1:109"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="cat_4.html#E2:109"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="cat_4.html#T80" target="_self" title="CAT_4:th.80">Th80</a></i>
<br/>.= 
<span class="p1"><a href="cat_4.html#K27" title="CAT_4:func.27">[$</a><span class="default"><font color="Maroon" title="c5">f</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="cat_1.html#K10" title="CAT_1:func.10">id</a> <font color="Maroon" title="c3">c</font></span>)</span> <a href="cat_1.html#K9" title="CAT_1:func.9">*</a> <font color="Maroon" title="c6">g</font></span>)</span></span><a href="cat_4.html#K27" title="CAT_4:func.27">$]</a></span>
<b>by </b><i><a class="txt" href="cat_4.html#E1:109"><i><font color="Green" title="E49">A1</font></i></a>, <a class="ref" href="cat_1.html#T57" title="CAT_1:th.57">CAT_1:57</a></i>
<br/>.= 
<span class="p1"><a href="cat_4.html#K27" title="CAT_4:func.27">[$</a><span class="default"><font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c6">g</font></span><a href="cat_4.html#K27" title="CAT_4:func.27">$]</a></span>
<b>by </b><i><a class="txt" href="cat_4.html#E2:109"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="cat_1.html#T57" title="CAT_1:th.57">CAT_1:57</a></i>
;<br/><br/>


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