From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6720 Path: news.gmane.org!not-for-mail From: Eduardo Dubuc Newsgroups: gmane.science.mathematics.categories Subject: size_question Date: Tue, 28 Jun 2011 14:39:10 -0300 Message-ID: Reply-To: Eduardo Dubuc NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1309292622 31493 80.91.229.12 (28 Jun 2011 20:23:42 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Tue, 28 Jun 2011 20:23:42 +0000 (UTC) To: Categories Original-X-From: majordomo@mlist.mta.ca Tue Jun 28 22:23:38 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.30]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1Qbeor-0004wD-UZ for gsmc-categories@m.gmane.org; Tue, 28 Jun 2011 22:23:38 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:34204) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Qbems-0004C3-Ma; Tue, 28 Jun 2011 17:21:34 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qbemr-0007r1-Up for categories-list@mlist.mta.ca; Tue, 28 Jun 2011 17:21:33 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6720 Archived-At: This is a naive question on non naive foundations. Consider the inclusion S_f C S of finite sets in sets. Is the category S_f closed under finite limits and at the same time small ? For example, there are a proper class of singletons, all finite. Thus a proper class of empty limits. Question, which is the small category of finite sets ?, which are its objects ?. A small site with finite limits for a topos would not be closed under finite limits ? etc etc But, more basic is the question above: How do you define the small category of finite sets ? Or only there are many small categories of finite sets ? You can not define a finite limit as being any universal cone because then you get a large category. Then how do you determine a small category with finite limits without choosing (vade retro !!) some of them. And if you choose, which ones ? The esqueleton is small but a different question !! e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]