From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4387 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Further to my question on adjoints Date: Mon, 12 May 2008 08:34:18 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1241019913 13072 80.91.229.2 (29 Apr 2009 15:45:13 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:45:13 +0000 (UTC) To: Categories list Original-X-From: rrosebru@mta.ca Mon May 12 12:07:44 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 12 May 2008 12:07:44 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1JvZMk-0005yn-5A for categories-list@mta.ca; Mon, 12 May 2008 11:51:02 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 10 Original-Lines: 17 Xref: news.gmane.org gmane.science.mathematics.categories:4387 Archived-At: 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