From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/7212 Path: news.gmane.org!not-for-mail From: Ignacio Lopez Franco Newsgroups: gmane.science.mathematics.categories Subject: when is Lex[A,V] abelian? Date: Wed, 22 Feb 2012 11:31:16 +0000 Message-ID: <87linv14vv.wl%ill20@cam.ac.uk> Reply-To: Ignacio Lopez Franco NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 (generated by SEMI 1.14.6 - "Maruoka") Content-Type: text/plain; charset=US-ASCII X-Trace: dough.gmane.org 1329918641 21973 80.91.229.3 (22 Feb 2012 13:50:41 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 22 Feb 2012 13:50:41 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Wed Feb 22 14:50:36 2012 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1S0CaZ-0004We-Pn for gsmc-categories@m.gmane.org; Wed, 22 Feb 2012 14:50:35 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:42711) by smtpx.mta.ca with esmtp (Exim 4.77) (envelope-from ) id 1S0CZa-0001o0-2i; Wed, 22 Feb 2012 09:49:34 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1S0CZZ-0003VN-Ha for categories-list@mlist.mta.ca; Wed, 22 Feb 2012 09:49:33 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:7212 Archived-At: Dear all, may be some of the readers of this list will know the answer to the following question. Let V be the category k-Mod for commutative ring k. For a finitely cocomplete V-category C, when is L = Lex[C^{op},V] abelian? I know some cases: 1. When C is abelian so is L. 2. When C is a free completion under finite colimits of a small category, L is abelian (because it's equivalent to a presheaf V-category). 3. L is reflective in the abelian [C^{op},V]. When the reflection is left exact L is abelian. However I don't any conditions that guaranty that the reflection is left exact. I would like to know some other conditions that ensure that L is abelian, and perhaps an example where L is not abelian. Thanks Ignacio [For admin and other information see: http://www.mta.ca/~cat-dist/ ]