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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E63">Th64</font></span>: <a NAME="T64"><span class="comment"><font color="firebrick">:: CAT_8:64</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">C1</font>, <font color="Olive" title="b2">C2</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="cat_6.html#NM2" title="CAT_6:NM.2">category</a><br/>  for <font color="Olive" title="b3">f</font> being   <a href="cat_6.html#NM1" title="CAT_6:NM.1">morphism</a> of <span class="p1">(<span class="default"><a href="cat_8.html#K14" title="CAT_8:func.14">Functors</a> (<font color="Olive" title="b1">C1</font>,<font color="Olive" title="b2">C2</font>)</span>)</span> holds <br/> ( <font color="Olive" title="b3">f</font> is  <a href="cat_6.html#V11" title="CAT_6:attr.11">identity</a>  iff  ex <font color="Olive" title="b4">F</font> being   <a href="cat_6.html#V16" title="CAT_6:attr.16">covariant</a>  <a href="cat_6.html#NM4" title="CAT_6:NM.4">Functor</a> of <font color="Olive" title="b1">C1</font>,<font color="Olive" title="b2">C2</font> st <font color="Olive" title="b3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Olive" title="b4">F</font>,<font color="Olive" title="b4">F</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>,<font color="Olive" title="b4">F</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> )</div></div>
