From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7005 Path: news.gmane.org!not-for-mail From: Dmitry Roytenberg Newsgroups: gmane.science.mathematics.categories Subject: Re: when does preservation of monos imply left exactness? Date: Wed, 26 Oct 2011 13:59:33 +0200 Message-ID: Reply-To: Dmitry Roytenberg NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: dough.gmane.org 1319635204 17038 80.91.229.12 (26 Oct 2011 13:20:04 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 26 Oct 2011 13:20:04 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Wed Oct 26 15:20:00 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 1RJ3Of-00068t-8d for gsmc-categories@m.gmane.org; Wed, 26 Oct 2011 15:19:58 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:47777) by smtpx.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1RJ3NX-0000GB-9n; Wed, 26 Oct 2011 10:18:47 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1RJ3NV-00060I-F3 for categories-list@mlist.mta.ca; Wed, 26 Oct 2011 10:18:45 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7005 Archived-At: I'll try again... On Mon, Oct 24, 2011 at 11:23 AM, Dmitry Roytenberg wrote: > Dear category theorists, > > It is well known that any functor that preserves finite limits > preserves monomorphisms, and that for an additive right-exact functor > between abelian categories, the converse is also true. Is it known how > far this extends to the non-additive setting? In other words, what > exactness properties of two categories and a functor between them > would suffice to conclude that the functor preserves finite limits if > and only if it preserves monos? For instance, is it enough to assume > that the categories be Barr-exact and that the functor preserve all > colimits, finite products and monos to conclude that it also preserves > equalizers? > > Any references would be extremely helpful. > > Thanks, > Dmitry > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]