Dear category theorists, let C be a monoidal category and S(C) the same category but regarded as a bicatgeory with a single object. Unless I am confused, a lax functor into S(C) is a lot like a sub-bicategory of the bicategory of bimodules internal to C. Identity morphisms a--Id-->a are sent by the lax functor to algebras A_a internal to C and morphisms a--->b to A_a-A_b bimodules. Composite morphisms a-->b-->c are sent to bimodule products over A_b. This, and in particular its precise formulation, must be well known. But I could not locate a reference for it. If anyone could provide any comments or point me to some literature, I'd be very grateful. P.S. This should play a role in defining the notion of background configurations is rational conformal field theory: http://golem.ph.utexas.edu/string/archives/000794.html