Re: Adjoints in bicategories

[Claudio Hermida <chermida@math.ist.utl.pt>]

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.