From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5033 Path: news.gmane.org!not-for-mail From: Toby Kenney Newsgroups: gmane.science.mathematics.categories Subject: Injective objects in topoi. Date: Fri, 26 Jun 2009 07:59:42 -0300 (ADT) Message-ID: Reply-To: Toby Kenney NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1246089538 14114 80.91.229.12 (27 Jun 2009 07:58:58 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 27 Jun 2009 07:58:58 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Sat Jun 27 09:58:51 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 1MKSoC-00069b-Sc for gsmc-categories@m.gmane.org; Sat, 27 Jun 2009 09:58:49 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1MKSIO-0002Fe-HR for categories-list@mta.ca; Sat, 27 Jun 2009 04:25:56 -0300 Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5033 Archived-At: Dear Category theorists, I'm sure the following lemma is either known, or I've made some mistake in proving it: Lemma: If I is an injective object in a topos, then for any monomorphism I>---m--->A, the object of splittings of m, i.e. S={f:I^A|(\forall i:I)(f(m(i))=i)} is also injective. Could someone let me know of a reference to it. Thanks a lot. Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]