From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5801 Path: news.gmane.org!not-for-mail From: Michael Shulman Newsgroups: gmane.science.mathematics.categories Subject: Re: Re: bilax_monoidal_functors Date: Fri, 14 May 2010 23:44:52 -0500 Message-ID: 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 1273945304 12830 80.91.229.12 (15 May 2010 17:41:44 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sat, 15 May 2010 17:41:44 +0000 (UTC) To: Original-X-From: categories@mta.ca Sat May 15 19:41:43 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 1ODLMo-0005dF-Vn for gsmc-categories@m.gmane.org; Sat, 15 May 2010 19:41:39 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1ODKxA-0006HZ-7J for categories-list@mta.ca; Sat, 15 May 2010 14:15:08 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5801 Archived-At: On Fri, May 14, 2010 at 8:05 PM, Joyal, Andre wrote: > I guess that in the category of R-modules over a commutative ring R, > a module M has a (good) dual iff it is finitely generated projective > iff the endo-functor functor Hom(M,-) preserves all colimits > (M is *compact* in a strong sense). Indeed, but in this case it is the objects of the category which are "compact," not the category itself. So if this is the argument, then a more natural term would be "locally compact" (clashing with "locally small," of course, but agreeing with "locally presentable" categories in which all objects are presentable). (I am *not* proposing to *actually* use "locally compact" -- I don't want to introduce yet another name for something that already has at least four names, even if none of the existing four are optimal.) Mike [For admin and other information see: http://www.mta.ca/~cat-dist/ ]