cocategory object in Bicat

Hi all, Let *2* be the category {0 <-- 1}. I would like the statement *2* is (the object of arrows of) a cocategory object in Bicat to make sense for some version of Bicat, and for some version of "cocategory object". What I have in mind is that given a bicategory B, the hom-bicategory [*2*,B] gives rise to some kind of double-category-like structure. One could consider eg equipments, double bicategories and the like arising from B, but what is going on with *2* to make this happen? Thanks, David -- David Roberts http://ncatlab.org/nlab/show/David+Roberts [For admin and other information see: http://www.mta.ca/~cat-dist/ ]