From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/342 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: a characterisation of factorisation systems Date: Tue, 18 Mar 1997 10:29:00 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241016903 25280 80.91.229.2 (29 Apr 2009 14:55:03 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:55:03 +0000 (UTC) To: categories Original-X-From: cat-dist Tue Mar 18 10:29:38 1997 Original-Received: by mailserv.mta.ca; id AA19515; Tue, 18 Mar 1997 10:29:00 -0400 Original-Lines: 37 Xref: news.gmane.org gmane.science.mathematics.categories:342 Archived-At: Date: 18 Mar 97 12:42:34 +0200 From: Hans Porst >Date: Fri, 14 Mar 1997 15:26:15 GMT >From: Paul-Andre Mellies Your definition >Let E and M be two classes of morphisms in a category C. >(E,M) is a factorisation system of C if and only if >the four following properties hold: > >1. every morphism f in C can be factored as f=me with m in M and e in E, >2. if e is a morphism in E and m is a morphism in M then e is orthogonal >to m, >3. if i is an iso left composable to e in E, then ie is in E, >4. if i is an iso right composable to m in M, then mi is in M. seems to be precisely the definition used in Adamek, Herrlich, Strecker: Abstract and Concrete Categories. Check their Chapter 14! AHS 14.6 shows in particular that E and M will be closed under composition. --------------------------------------------------------- Hans-E. Porst e-mail: porst@mathematik.uni-bremen.de FB 3: Mathematik Phone: +49 421 2182276 University of Bremen +49 421 2184971 D-28334 Bremen Fax: +49 421 2184856 ---------------------------------------------------------