From mboxrd@z Thu Jan 1 00:00:00 1970
X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7649
Path: news.gmane.org!not-for-mail
From: Paul Levy
Newsgroups: gmane.science.mathematics.categories
Subject: Re: Reference: equivalences can be made into adjunctions
Date: Mon, 8 Apr 2013 08:57:37 +0100
Message-ID:
References:
Reply-To: Paul Levy
NNTP-Posting-Host: plane.gmane.org
Mime-Version: 1.0 (Apple Message framework v936)
Content-Type: text/plain; charset=UTF-8; format=flowed; delsp=yes
Content-Transfer-Encoding: quoted-printable
X-Trace: ger.gmane.org 1365438251 25117 80.91.229.3 (8 Apr 2013 16:24:11 GMT)
X-Complaints-To: usenet@ger.gmane.org
NNTP-Posting-Date: Mon, 8 Apr 2013 16:24:11 +0000 (UTC)
Cc: categories list
To: =?UTF-8?Q?Jonathan_CHICHE_=E9=BD=8A=E6=AD=A3=E8=88=AA?=
Original-X-From: majordomo@mlist.mta.ca Mon Apr 08 18:24:12 2013
Return-path:
Envelope-to: gsmc-categories@m.gmane.org
Original-Received: from smtp3.mta.ca ([138.73.1.186])
by plane.gmane.org with esmtp (Exim 4.69)
(envelope-from )
id 1UPErO-0002AI-Aj
for gsmc-categories@m.gmane.org; Mon, 08 Apr 2013 18:23:58 +0200
Original-Received: from mlist.mta.ca ([138.73.1.63]:37547)
by smtp3.mta.ca with esmtp (Exim 4.80)
(envelope-from )
id 1UPBlE-0006m1-BZ; Mon, 08 Apr 2013 10:05:24 -0300
Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71)
(envelope-from )
id 1UPBlC-0007jq-VJ
for categories-list@mlist.mta.ca; Mon, 08 Apr 2013 10:05:22 -0300
In-Reply-To:
Precedence: bulk
Xref: news.gmane.org gmane.science.mathematics.categories:7649
Archived-At:
On 6 Apr 2013, at 21:22, Jonathan CHICHE =E9=BD=8A=E6=AD=A3=E8=88=AA =
wrote:
> Dear all,
>
> This is a standard fact, proved for instance in details in =20
> "Categories for the Working Mathematician" (Chapter 4, Section 4, =20
> Theorem 1 in the second edition), that a functor is an equivalence =20
> of categories if and only if it is part of an adjoint equivalence. I =20=
> would like to use the fact that this is true in an arbitrary 2-=20
> category, i.e. that given an equivalence in a 2-category the =20
> invertible 2-cells can be required to satisfy the triangle =20
> identities. Is there a standard reference for this fact?
Dear Jonathan,
A reference is "Two-dimensional monad theory" by Blackwell, Kelly and =20=
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/ ]