Dear categorists, suppose V is a monoidal category, with underlying category V_0, and X is an ordinary category. Then (if I am not mistaken) the functor category V_0^X has a monoidal structure, defined point-wise by that of V and each functor f:X->Y gives a strong monoidal functor. First question : supposing V closed, under which hypothesis is V_0^X closed as well (as in the case V = Set)? Second question: supposing that V_0^X is indeed closed and that V is suitably complete, so that reindexing along f has a right adjoint forall_f, then V_0^X is enriched over V by forall_X(A->B). How is this enrichment related to the usual one of [X,v] when X is a V-category? Best regards, Claudio [For admin and other information see: http://www.mta.ca/~cat-dist/ ]