From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7023 Path: news.gmane.org!not-for-mail From: Dmitry Roytenberg Newsgroups: gmane.science.mathematics.categories Subject: Re: Re: when does preservation of monos imply left exactness? Date: Mon, 31 Oct 2011 11:45:14 +0100 Message-ID: References: Reply-To: Dmitry Roytenberg NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1320065502 28688 80.91.229.12 (31 Oct 2011 12:51:42 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 31 Oct 2011 12:51:42 +0000 (UTC) Cc: Steve Lack , richard.garner@mq.edu.au, categories@mta.ca To: George Janelidze Original-X-From: majordomo@mlist.mta.ca Mon Oct 31 13:51:38 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1RKrKx-0006T5-7M for gsmc-categories@m.gmane.org; Mon, 31 Oct 2011 13:51:35 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:35915) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1RKrJy-0000jc-KS; Mon, 31 Oct 2011 09:50:34 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RKrJw-0002P9-UA for categories-list@mlist.mta.ca; Mon, 31 Oct 2011 09:50:32 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7023 Archived-At: Dear George, Well, I find Barr's theorem useful insomuch as it highlights regular monos as the relevant ones and thereby brings the situation into sharper focus: proving the preservation of the equalizers of cokernel pairs should be easier than arbitrary ones. Of course, characterizing the regular monos and proving that they are preserved by cobase change (I've finally remembered what A@- is called!) could be a difficult matter, depending on the circumstances. So, I thank everyone for the feedback. I will post here if I manage to prove anything of interest. Best, Dmitry On Sun, Oct 30, 2011 at 1:10 AM, George Janelidze wro= te: > Dear Dmitry, > > Absolutely correct (although it does not change anything I said). > > Thank you for explaining "why". So your real question is about preservati= on > of finite limits by functors of the form A+(-), in the case non-commutati= ve > algebras (of various kinds). Well, from this point of view the categories= of > algebras are 'difficult', and I don't recall any reasonable result at the > moment. Moreover, I am surprised that Barr's theorem helps here (which do= es > not mean that the theorem itself is not good of course!), and I would be > very interested to learn, what exactly could you deduce from it? > > Best regards, > > George > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]