From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5869 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Equality again Date: Thu, 27 May 2010 12:30:09 +0100 (BST) Message-ID: References: Reply-To: "Prof. Peter Johnstone" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=iso-8859-1; format=flowed Content-Transfer-Encoding: QUOTED-PRINTABLE X-Trace: dough.gmane.org 1275151449 25858 80.91.229.12 (29 May 2010 16:44:09 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 29 May 2010 16:44:09 +0000 (UTC) To: =?ISO-8859-15?Q?Andr=E9_Joyal?= Original-X-From: categories@mta.ca Sat May 29 18:43:57 2010 connect(): No such file or directory Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OIP8e-0004sL-KW for gsmc-categories@m.gmane.org; Sat, 29 May 2010 18:43:56 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OIOZR-0005XA-QX for categories-list@mta.ca; Sat, 29 May 2010 13:07:33 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5869 Archived-At: On Mon, 24 May 2010, Joyal, Andr=E9 wrote: > I love the equality symbol more than an isomorphism symbol, > and an isomorphism symbol more than an equivalence symbol. > I always try to use the equality symbol whenever possible. > I often use the equality symbol for a canonical isomorphism. > Is there a special symbol for canonical isomorphism? (as oppose > to a plain isomorphism). I would love to write something like > > A times (B times C) =3D' (A times B) times C > > Andr=E9 > TeX provides a command \doteq for an equality sign with a dot over it; this is used in other areas of mathematics to mean "is approximately equal to", but as far as I know it hasn't yet been used by=20 category-theorists. Perhaps we could use it to mean "is canonically isomorphic to"? I'd also like to use it (or something like it) between pairs of morphisms, meaning that (they are not equal but) they become equal when composed with the appropriate canonical isomorphisms (to which I can't be bothered to give names) in order to match up their domains and codomains. (Of course, this is simply saying that they are canonically isomorphic as objects of the functor category [2,C], where C is the category in which they live.) Peter Johnstone [For admin and other information see: http://www.mta.ca/~cat-dist/ ]