From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/99 Path: news.gmane.org!not-for-mail From: "Serge P. Kovalyov" Newsgroups: gmane.science.mathematics.categories Subject: Question on E-coreflective subcategories Date: Wed, 18 Feb 2009 22:23:14 +0600 (NOVT) Message-ID: Reply-To: "Serge P. Kovalyov" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1235008006 23416 80.91.229.12 (19 Feb 2009 01:46:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 19 Feb 2009 01:46:46 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Thu Feb 19 02:48:01 2009 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 4.50) id 1LZy1A-0001dN-Bw for gsmc-categories@m.gmane.org; Thu, 19 Feb 2009 02:48:00 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LZxHo-0006bC-Lp for categories-list@mta.ca; Wed, 18 Feb 2009 21:01:08 -0400 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:99 Archived-At: Dear Category Theory gurus, In my reserach I have encountered the following problem. Let A be a full isomorphism-closed coreflective subcategory of a category C, G : C -> A be a coreflection. Let (E, M) be a factorization system for C-morphisms, such that class G(E) contains class of all A-isomorphisms and is contained in class of all A-retractions. Is any of the following statements correct: 1. If functor G preserves M, then it preserves E. 2. If any M-morphism is mono, then an M-morphism belongs to Mor(A) provided that its codomain belongs to Ob(A). Examples known to me satisfy both statements, but I fail to prove any. Thanks, Serge.