I am looking at the Yoneda lemma trying to see where the assumption of "locally small" really comes in. Obviously in order to define a functor to the category sets using $Hom$-spaces we need our $Hom$-spaces to be sets. However if we consider a enriched-category, enriched over some monoidal category M, then for any element of the category, our $Hom$-sets give us a functor $Hom(A,-)$ to M. The Yoneda lemma is usually described as a "totally formal" result, so perhaps it holds for a general monoidal category? If not what do we need to assume on M for Yoneda to work?