This thing still confuses me. And it seems every reference I look at states it entirely differently. I guess I've heard it stated in words -- there is a full embedding of C in Funct(Cop, Set). I know what all of the words mean, but I'm not sure if that helps yet. There's one particular application of it that interests me, and I can't really see how to use it: there's a proof that shows the existance of a natural transformation Hom(_, A) --> Hom(_, B). From this, they then conclude (by the Yoneda lemma!) that this natural transformation must come from a uniquely determined map A --> B. (The existance of this map is what interests me) How does that follow?