Dear colleagues, I'm looking for a reference where the following fact (that I believe to be clearly true) is discussed: Let V and C be biclosed monoidal categories. Suppose that V is symmetric and that we have a strong braided monoidal functor z : V --> Z(C) to the center of C in the sense of Joyal-Street. Assume further that the functor z(-) \otimes Y : V --> C has a right adjoint Hom(Y,-) : C --> V for any object Y in C. Then C is a monoidal V-category with Hom objects in V given by this right adjoint. You may assume that V and C are (co)complete if you wish. It is easy to construct compositions morphisms, etc. in an elementary way, but verifying all laws is a pain. This is why I'm willing to find a reference. All the best for the new year, Fernando Muro [For admin and other information see: http://www.mta.ca/~cat-dist/ ]