Dear List, The weakest form of limits in a bicategory are defined by equivalences of hom-categories in place of the slightly more strict version defined by isomorphisms. Then the process of defining a monoidal structure on a bicategory with finite products takes on a slightly different flavor in each case. In the weak case, given a pair of 1-cells one must *choose* a monoidal product, whereas in the latter case, a *unique choice* of monoidal product can be obtained from the one-dimensional aspect of the universal property. I would guess that in the former case, one should not worry too much about how to choose the product 1-cells, since the universal property will come to the rescue when checking that one has indeed defined a monoidal structure on the bicategory. Does anyone know of a reference which proves something along these lines? Best, Alex [For admin and other information see: http://www.mta.ca/~cat-dist/ ]