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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E68">Def30</font></span>   defines <a href="cat_8.html#V8" title="CAT_8:attr.8">with_exponential_objects</a> <a onclick="hs(this)" href="javascript:()">CAT_8:def 30 : <br/></a><span> for <font color="Olive" title="b1">C</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="cat_8.html#V7" title="CAT_8:attr.7">with_binary_products</a>  <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a> holds <br/> ( <font color="Olive" title="b1">C</font> is  <a href="cat_8.html#V8" title="CAT_8:attr.8">with_exponential_objects</a>  iff  for <font color="Olive" title="b2">a</font>, <font color="Olive" title="b3">b</font> being   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Olive" title="b1">C</font>  ex <font color="Olive" title="b4">c</font> being   <a href="cat_6.html#NM3" title="CAT_6:NM.3">Object</a> of <font color="Olive" title="b1">C</font> ex <font color="Olive" title="b5">e</font> being    <a href="cat_7.html#M1" title="CAT_7:mode.1">Morphism</a> of <font color="Olive" title="b4">c</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> st <br/>(  <a href="cat_7.html#K2" title="CAT_7:func.2">Hom</a> (<span class="p1">(<span class="default"><font color="Olive" title="b4">c</font> <a href="cat_8.html#K4" title="CAT_8:func.4">[x]</a> <font color="Olive" title="b2">a</font></span>)</span>,<font color="Olive" title="b3">b</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>  &amp; <font color="Olive" title="b4">c</font>,<font color="Olive" title="b5">e</font> <a href="cat_8.html#R5" title="CAT_8:pred.5">is_exponent_of</a> <font color="Olive" title="b2">a</font>,<font color="Olive" title="b3">b</font> ) );<br/></span></div>
