From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5652 Path: news.gmane.org!not-for-mail From: Thomas Streicher Newsgroups: gmane.science.mathematics.categories Subject: Re: equality is beautiful Date: Mon, 22 Mar 2010 10:17:36 +0100 Message-ID: References: Reply-To: Thomas Streicher NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: dough.gmane.org 1269270933 1130 80.91.229.12 (22 Mar 2010 15:15:33 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 22 Mar 2010 15:15:33 +0000 (UTC) Cc: Richard Garner , categories@mta.ca To: David Leduc Original-X-From: categories@mta.ca Mon Mar 22 16:15:27 2010 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 4.69) (envelope-from ) id 1NtjLh-0005y8-O5 for gsmc-categories@m.gmane.org; Mon, 22 Mar 2010 16:15:25 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1NtiqK-0006T4-Jf for categories-list@mta.ca; Mon, 22 Mar 2010 11:43:00 -0300 Content-Disposition: inline In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5652 Archived-At: > What about the characterization of limits in terms of products and > equalizers? It states that the limit of a functor F:J->C is > constructed by products indexed by the set(oid) of objects and the > set(oid) of arrows of J. But if you don't allow equality on objects in > J, you only have a preset of object, not a set(oid). I don't see a problem here. Usually one speaks about small limits, i.e. limits of diagrams whose shape is a small category. But small categories are categories internal to the base. Now under the quite common assumption that this base has finite limits one can speak about equality of objects in the shape of the diagram. Thomas [For admin and other information see: http://www.mta.ca/~cat-dist/ ]