Frank Atanassow wrote:
I'm looking for definitions of (the weak 2-dimensional analogues of 1-) products and coproducts for bicategories, and also adjoints. In his 1967 article "Introduction to Bicategories, Part I" Benabou promises to treat biadjoints in a sequel, but I gather this was never published. Gray treats a notion of "quasi-adjointness" in "Formal Category Theory"; is this accepted as the "right" generalization?
Pointers to definitions of these concepts in one of the approaches to weak n-categories would be welcome as well.
Relevant references: Kelly, G. M. Elementary observations on $2$-categorical limits. Bull. Austral. Math. Soc. 39 (1989), no. 2, 301--317. Power, A. J. Coherence for bicategories with finite bilimits. I. Categories in computer science and logic (Boulder, CO, 1987),341--347, Contemp. Math., 92, Amer. Math. Soc., Providence, RI, 1989. Betti, Renato; Power, A. John On local adjointness of distributive bicategories. Boll. Un. Mat. Ital. B (7) 2 (1988), no. 4, 931--947. Bird, G. J.; Kelly, G. M.; Power, A. J.; Street, R. H. Flexible limits for $2$-categories. J. Pure Appl. Algebra 61 (1989), no. 1, 1--27.