From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2426 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: Uniform spaces Date: Wed, 27 Aug 2003 16:21:34 -0400 (EDT) Message-ID: References: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018651 4112 80.91.229.2 (29 Apr 2009 15:24:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:24:11 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Aug 28 08:37:18 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 28 Aug 2003 08:37:18 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19sL3p-0000K1-00 for categories-list@mta.ca; Thu, 28 Aug 2003 08:35:29 -0300 In-Reply-To: Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 18 Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:2426 Archived-At: Any study of the category must begin with Isbell's wonderful book on the subject. Although John's exposition could be difficult, it was not so in that book. I don't recall about limits and colimits (but they ought to be easy), but there is a lot of discussion of internal homs (which do not always exist and are not symmetric when they do). The category is not cartesian closed. I am pretty sure the forgetful functor to Top has a left adjoint and therefore preserves limits. It preserves sums for sure, but not coequalizers since a quotient space of a hausdorff uniform space can be hausdorff without being completely regular. At least, that is what I think I remember. Michael On Wed, 27 Aug 2003, Tom Leinster wrote: > Hello, > > Does anyone know of any account of the basic properties of the category of > uniform spaces? I'm after things like (co)limits, cartesian closure, and > (co)limit-preservation by the forgetful functor to Top. Bourbaki gets me > some of the way, but his decision not to use categorical language and > the resulting circumlocutions make it a struggle. > > Thanks, > Tom > > > >