Re: Reference: equivalences can be made into adjunctions

[Paul Levy <P.B.Levy@cs.bham.ac.uk>]

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












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