Super Yoneda?

We all know that if Hom(A,-) is naturally equivalent to Hom(B,-), then A is isomorphic to B. But can you find a category in which for each object C, Hom(A,C) is isomorphic to Hom(B,C) but no naturality of the isomorphism without A being isomorphic to B? Michael [For admin and other information see: http://www.mta.ca/~cat-dist/ ]