From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5794 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: Re: bilax_monoidal_functors Date: Thu, 13 May 2010 12:17:48 -0500 Message-ID: References: Reply-To: Michael Shulman NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1273843284 2941 80.91.229.12 (14 May 2010 13:21:24 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 14 May 2010 13:21:24 +0000 (UTC) To: Jeff Egger Original-X-From: categories@mta.ca Fri May 14 15:21:23 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 1OCupO-00038U-3F for gsmc-categories@m.gmane.org; Fri, 14 May 2010 15:21:22 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1OCuKA-0002N8-9l for categories-list@mta.ca; Fri, 14 May 2010 09:49:06 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5794 Archived-At: On Mon, May 10, 2010 at 2:28 PM, Jeff Egger wrote: > the fact that "autonomous category" is a special case (and, from one > point of view, a rather uninteresting special case) of > "star-autonomous category", whereas it sounds like "star-autonomous > category" should mean an "autonomous category" with some extra > structure. I agree, it does sound like that, but there is at least a long tradition of such names in mathematics (not that that makes them a good thing). (http://ncatlab.org/nlab/show/red+herring+principle) One reason I like "autonomous" to mean a symmetric monoidal category in which all objects have duals is that the only alternative names I have heard for such a thing convey misleading intuition to me. They are sometimes called "compact closed" or (I think) "rigid" monoidal categories, but "compact" and "rigid" are words with definite and inapplicable intuitive meanings for me. Compact means small, finite, bounded, inaccessible by directed joins, etc. and "rigid" means "having few automorphisms," and I don't see that there is anything very compact or rigid about such categories. The only relationship I can think of is that a compact subset of a Hausdorff space is closed, and a symmetric monoidal category with duals for objects is also automatically closed, but of course these two meanings of "closed" are totally different. Perhaps someone can enlighten me? Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]