In response to Michael Barr's question: Theorem: If V is a closed braided monoidal category which is complete and cocomplete then the bicategory V-Mod of V-categories, V-modules (sometimes called V-bimodules, V-distributors or V-profunctors), and V-module morphisms is a monoidal bicategory (meaning the hom of a tricategory with one object). However, in order for V-Mod to be braided, V must be symmetric in which case V-Mod is also symmetric (also called strongly involutory by Baez-Dolan). If you are only interested in monoids in V, just take the subbicategory of one-object V-categories. Of course, then, you can do with less completeness and cocompleteness on V. But yes, the detailed proof of this makes a long, but fairly routine, story. Brian Day and I are working on a paper "Monoidal bicategories and Hopf algebroids" which will contain a discreet amount of detail (along with other things). I have been talking about aspects of the paper in our Category Seminars. Regards, Ross