Let 

> $F:A^{\mbox{op}} \to \mbox{Set}$

and define 

> $G_a:A\times A^{\mbox{op}} \to \mbox{Set}$

> $G_a(b,c) = \mbox{hom}(a,b) \times F(c)$.  

I <i>think</i> the coend of $G_a$, 

> $\int^AG_a$, 

ought to be $F(a)$--it's certainly true when A is discrete, since then hom is a delta function.  But my colimit-fu isn't good enough to actually compute the thing and verify it's true.  Can someone walk me through the computation, please?