From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3319 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: regular monos not closed under composition Date: Wed, 17 May 2006 10:47:01 +0100 (BST) Message-ID: <4343.04920859194$1241019227@news.gmane.org> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241019226 8223 80.91.229.2 (29 Apr 2009 15:33:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:33:46 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed May 17 13:13:37 2006 -0300 X-Keywords: X-UID: 263 Original-Lines: 18 Xref: news.gmane.org gmane.science.mathematics.categories:3319 Archived-At: On Tue, 16 May 2006, Thomas Streicher wrote: > I know that regular monos needn't be closed under composition. One example > being the category of monoids. Are there other *natural* examples, e.g. of > topological kind? > > Thomas Streicher > Depends what you mean by topological. In the category of locales, regular epis aren't closed under composition (equivalently, regular monos aren't closed under composition in frames): this was proved by Till Plewe, and is in his paper `Quotient maps of locales' in Appl. Cat. Struct. 8 (2000), 17--44. Another `natural' example (which I regularly use when teaching category theory to graduate students) is regular epis in Cat. Peter Johnstone