From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4388 Path: news.gmane.org!not-for-mail From: Eduardo Dubuc Newsgroups: gmane.science.mathematics.categories Subject: Re: Further to my question on adjoints Date: Mon, 12 May 2008 12:43:55 -0300 (ART) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019914 13077 80.91.229.2 (29 Apr 2009 15:45:14 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:45:14 +0000 (UTC) To: categories@mta.ca (Categories list) Original-X-From: rrosebru@mta.ca Tue May 13 14:15:08 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 13 May 2008 14:15:08 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Jvxq6-0005p2-NJ for categories-list@mta.ca; Tue, 13 May 2008 13:58:58 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 11 Original-Lines: 32 Xref: news.gmane.org gmane.science.mathematics.categories:4388 Archived-At: Consider the dual finitary question: In universal algebra in order to show that finitely presented objects are closed under coequalizers it is essential that a amorphism of finitely presented objects lift to a morphism between the free. Is this the only way to prove it ? : " but when I look at examples, it has turned out to be true for other reasons." greetings e.d. > > In March I asked a question on adjoints, to which I have received no > correct response. Rather than ask it again, I will pose what seems to be > a simpler and maybe more manageable question. Suppose C is a complete > category and E is an object. Form the full subcategory of C whose objects > are equalizers of two arrows between powers of E. Is that category closed > in C under equalizers? (Not, to be clear, the somewhat different question > whether it is internally complete.) > > In that form, it seems almost impossible to believe that it is, but it is > surprisingly hard to find an example. When E is injective, the result is > relatively easy, but when I look at examples, it has turned out to be true > for other reasons. Probably there is someone out there who already knows > an example. > > Michael > >