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*To*: categories@mta.ca*Subject*: categories: Re: Adjoints in bicategories*From*: John MacDonald <johnm@math.ubc.ca>*Date*: Thu, 22 Jun 2000 14:52:28 -0600*In-Reply-To*: <20000622124507.EF71C451D@mail.cs.uu.nl>*Sender*: cat-dist@mta.ca

In reply to Frank Atanassow's question: Here is a list of a few references I have on hand that are related or somewhat related to your question. This list is not intended to be complete and I hope others will add more references and/or details. John MacDonald, Department of Mathematics University of British Columbia Vancouver, B.C., Canada V5K 1N4 [1] R. Blackwell, G.M.Kelly, J.Power, Two-Dimensional Monad Theory, Sydney Category Seminar Reports 1987. [2] M.C.Bunge, Coherent Extensions and Relational Algebras, Trans. Amer. Math. Soc.197(1974), 355-390. [3] J.W.Gray, Formal Category Theory: Adjointness for 2-Categories, Lecture Notes in Mathematics 391, Springer-Verlag 1974. [4] C.B.Jay, Local Adjunctions, Journal of Pure and Applied Algebra 53(1988), 227-238 [5] G.M.Kelly, Elementary Observations on 2-Categorical Limits, Bull. Austral. Math. Soc. 39(1989), 301-317 [6] G.M.Kelly, R.H.Street, Review of the Elements of 2-Categories, Lecture Notes in Mathematics 420, Springer-Verlag 1974, 75-109. [7] J.L.MacDonald, A.Stone, Soft Adjunction between 2-Categories, Journal of Pure and Applied Algebra 60(1989), 155-203. [8] R.H.Street, The formal Theory of Monads, Journal of Pure and Applied Algebra 2(1972),149-168. At 02:45 PM 6/22/00 +0200, you 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. > >-- >Frank Atanassow, Dept. of Computer Science, Utrecht University >Padualaan 14, PO Box 80.089, 3508 TB Utrecht, Netherlands >Tel +31 (030) 253-1012, Fax +31 (030) 251-3791

**References**:**categories: Adjoints in bicategories***From:*Frank Atanassow <franka@cs.uu.nl>

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