From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6113 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: Dual category and dual object Date: Sat, 4 Sep 2010 17:54:43 -0700 Message-ID: References: Reply-To: Toby Bartels NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: dough.gmane.org 1283701386 31658 80.91.229.12 (5 Sep 2010 15:43:06 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Sun, 5 Sep 2010 15:43:06 +0000 (UTC) Cc: Michael Barr To: categories Original-X-From: majordomo@mlist.mta.ca Sun Sep 05 17:43:05 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.139]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1OsHN0-0004PS-O7 for gsmc-categories@m.gmane.org; Sun, 05 Sep 2010 17:43:02 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:41059) by smtpy.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1OsHLi-0007iq-U1; Sun, 05 Sep 2010 12:41:43 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1OsHLe-0005OL-Lt for categories-list@mlist.mta.ca; Sun, 05 Sep 2010 12:41:39 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6113 Archived-At: Michael Barr wrote: >Toby Bartels wrote: >>David Leduc wrote: >>>Are the notions of dual category and dual object related? >>On the other hand, we can say "opposite category" instead of "dual category", >>especially since we denote the dual category of C by C^{op}. >So you would say that complete atomic boolean algebras is just Set^{op}? >Well I wouldn't. They are, of course, equivalent, but the same. I would say both "The dual category of Set is Set^{op}." and "CABA is a dual category of Set." (and also "CABA is an opposite category of Set."). Actually, I would probably do the grammar differently: "CABA is a category dual [or "opposite"] to Set.". Leduc's original question didn't have an article in it; you seem to have interpreted is with "a" while I interpreted it with "the". (We also interpreted "dual object" differently.) --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]