From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4335 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: A question on adjoints Date: Tue, 18 Mar 2008 13:11:44 -0500 (EST) 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 1241019878 12802 80.91.229.2 (29 Apr 2009 15:44:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:44:38 +0000 (UTC) To: Categories list Original-X-From: rrosebru@mta.ca Tue Mar 18 19:03:07 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 18 Mar 2008 19:03:07 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1Jbjo3-0007W5-BJ for categories-list@mta.ca; Tue, 18 Mar 2008 18:57:15 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 99 Original-Lines: 13 Xref: news.gmane.org gmane.science.mathematics.categories:4335 Archived-At: I guess I am getting old and dumb. This question should have been a snap for me years ago. It is old fashioned, only a 1-categorical question and not about internal vs. external. Suppose F: A --> B is left adjoint to U: B --> A. Suppose a is an object of A and b, b' objects of B such that there is an equalizer a ---> Ub ===> Ub'. (The two arrows Ub to UB' are not assumed to be U of arrows from B.) Does it follow that a ---> UFa ===> UFUFa is an equalizer? The arrows are \eta a, UF\eta a and \eta UFa of course. Michael