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<a NAME="E1:62_3_1"/>
 ex <font color="Olive">B</font> being non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V6">strict</a> <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">W</font> <a href="waybel34.html#K5" target="_self">-SUP_category</a>  st <br/>( ( for <font color="Olive">a</font> being  <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="waybel34.html#K5" target="_self">-SUP_category</a> </span>)</span> holds <br/> ( <font color="Olive">a</font> is   <a href="altcat_1.html#NM1">object</a> of <font color="Olive">B</font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">a</font>] ) ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="waybel34.html#K5" target="_self">-SUP_category</a> </span>)</span><br/> for <font color="Olive">a'</font>, <font color="Olive">b'</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Olive">B</font>  st <font color="Olive">a'</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b'</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">f</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font> holds <br/> ( <font color="Olive">f</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">a'</font>,<font color="Olive">b'</font></span><a href="altcat_1.html#K1">^&gt;</a></span> iff <font color="Maroon">S<sub>2</sub></font>[<font color="Olive">a</font>,<font color="Olive">b</font>,<font color="Olive">f</font>] ) ) )
 
<b>from </b><i><a class="ref" href="yellow18.html#S7">YELLOW18:sch 7</a>(, , );<br/></i>
<b>hence </b><a NAME="E2:62_3_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V6">strict</a> <a href="altcat_2.html#NM2">subcategory</a> of <font color="Maroon">W</font> <a href="waybel34.html#K5" target="_self">-SUP_category</a>  st <br/>( ( for <font color="Olive">a</font> being  <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="waybel34.html#K5" target="_self">-SUP_category</a> </span>)</span> holds  <font color="Olive">a</font> is   <a href="altcat_1.html#NM1">object</a> of <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">a</font>, <font color="Olive">b</font> being  <a href="altcat_1.html#NM1">object</a> of <span class="p1">(<span class="default"><font color="Maroon">W</font> <a href="waybel34.html#K5" target="_self">-SUP_category</a> </span>)</span><br/> for <font color="Olive">a'</font>, <font color="Olive">b'</font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Olive">b<sub>1</sub></font>  st <font color="Olive">a'</font> <a href="hidden.html#R1">=</a> <font color="Olive">a</font> &amp; <font color="Olive">b'</font> <a href="hidden.html#R1">=</a> <font color="Olive">b</font> &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">a</font>,<font color="Olive">b</font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">f</font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">a</font>,<font color="Olive">b</font> holds <br/> ( <font color="Olive">f</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">a'</font>,<font color="Olive">b'</font></span><a href="altcat_1.html#K1">^&gt;</a></span> iff  <a href="waybel34.html#K2" target="_self">UpperAdj</a> <span class="p1">(<span class="default"><a href="yellow21.html#K5">@</a> <font color="Olive">f</font></span>)</span> is <a href="waybel_0.html#V22">directed-sups-preserving</a> ) ) )
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