From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6786 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: size_question_encore Date: Wed, 13 Jul 2011 21:10:51 -0700 Message-ID: References: Reply-To: Toby Bartels NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: dough.gmane.org 1310689264 31143 80.91.229.12 (15 Jul 2011 00:21:04 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 15 Jul 2011 00:21:04 +0000 (UTC) To: Categories Original-X-From: majordomo@mlist.mta.ca Fri Jul 15 02:20:59 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpy.mta.ca ([138.73.1.128]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1QhW9L-0000t8-GW for gsmc-categories@m.gmane.org; Fri, 15 Jul 2011 02:20:59 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:52204) by smtpy.mta.ca with esmtp (Exim 4.76) (envelope-from ) id 1QhW6p-0008FD-Gv; Thu, 14 Jul 2011 21:18:23 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QhW6o-0002f1-N8 for categories-list@mlist.mta.ca; Thu, 14 Jul 2011 21:18:22 -0300 Content-Disposition: inline In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6786 Archived-At: Mike Shulman wrote in part: >Even in a category of sets, I don't see why choice is necessary in >order to complete a small subcategory under finite limits and obtain a >small subcategory. It seems to me that what is needed is rather the >axiom of collection, which implies that we can find some *set* of >objects containing *at least one* limit for every finite diagram in >the original small subcategory; and then we can iterate countably many >times to obtain a small category which contains at least one limit for >any finite diagram therein. The axiom of collection guarantees only *some* appropriate set of objects, so you need to choose one. To iterate this countably many times, you might need dependent choice. Unless I'm not understanding what you're doing. --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]