From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5814 Path: news.gmane.org!not-for-mail From: selinger@mathstat.dal.ca (Peter Selinger) Newsgroups: gmane.science.mathematics.categories Subject: Re: terminology Date: Sun, 16 May 2010 09:44:08 -0300 (ADT) Message-ID: Reply-To: selinger@mathstat.dal.ca (Peter Selinger) NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1274031507 9717 80.91.229.12 (16 May 2010 17:38:27 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 16 May 2010 17:38:27 +0000 (UTC) To: categories@mta.ca (Categories List) Original-X-From: categories@mta.ca Sun May 16 19:38:26 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 1ODhnF-0006Br-Ri for gsmc-categories@m.gmane.org; Sun, 16 May 2010 19:38:26 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1ODhYx-0001Hv-0t for categories-list@mta.ca; Sun, 16 May 2010 14:23:39 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5814 Archived-At: I had written: >=20 > My last comment is that, unlike what Jeff Egger claimed, "autonomous > category" is not a special case of "*-autonomous category", because no > symmetry is assumed in autonomous categories. Unless of course one > first drops symmetry from the definition of *-autonomous categories, > as Jeff has also suggested. As it stands, neither of "autonomous" and > "*-autonomous" implies the other, which is perfectly fine in my > opinion, since they are two different words. I would like to clarify that Jeff himself did not say anything false, because in the context in which he said it, he had in fact assumed the non-symmetric definition of *-autonomous category (of [Barr 1995]). Sorry if it sounded like I was accusing him. My intention was only to point out that the statement "autonomous categories are a special case of *-autonomous categories" cannot be quoted out of context, because it is false under the original definition of *-autonomous category that includes symmetry (of [Barr 1979]). Since it had already been quoted out of context when I wrote the above, I just wanted to point out how the potential confusion.=20 I think this is a very apt illustration of what happens if a term with an existing meaning is redefined to mean something else. Henceforth it is impossible for anybody to use the term (with either meaning) without first giving a definition. That's no problem in a math paper, where definitions are usually given or cited anyway, and therefore terminology is in principle arbitrary. But it does tend to hobble everyday discussion. -- Peter P.S.: since I have a demonstrated ability to put my foot in my mouth, I'd like to clarify that I am not accusing Mike Barr of anything either. His 1995 paper is clearly entitled "Non-symmetric *-autonomous categories", and the inside of the paper clearly explains the distinction. It is only in subsequent use that any confusion arises. The usual solution, of putting either (non-symmetric) or (symmetric) in parentheses the first time the term is used, and omitting it for subsequent uses, is perfectly adequate. I am very happy with the statement "an autonomous category is a special case of a (non-symmetric) *-autonomous category". M. Barr (1979). "*-Autonomous Categories", Lectures Notes in Mathematics 752. Springer.=20 M. Barr (1995). "Non-symmetric *-autonomous categories".=20 Theoretical Computer Science 139:115=E2=80=93130. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]