On 6 Apr 2013, at 21:22, Jonathan CHICHE 齊正航 wrote:
Dear all,
This is a standard fact, proved for instance in details in "Categories for the Working Mathematician" (Chapter 4, Section 4, Theorem 1 in the second edition), that a functor is an equivalence of categories if and only if it is part of an adjoint equivalence. I would like to use the fact that this is true in an arbitrary 2- category, i.e. that given an equivalence in a 2-category the invertible 2-cells can be required to satisfy the triangle identities. Is there a standard reference for this fact?
Dear Jonathan, A reference is "Two-dimensional monad theory" by Blackwell, Kelly and Power. Journal of Pure and Applied Algebra 59, 1989. I asked a similar question in 2001: http://facultypages.ecc.edu/alsani/ct01%289-12%29/msg00071.html which led to some very interesting responses. Paul -- Paul Blain Levy School of Computer Science, University of Birmingham +44 121 414 4792 http://www.cs.bham.ac.uk/~pbl [For admin and other information see: http://www.mta.ca/~cat-dist/ ]