From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6725 Path: news.gmane.org!not-for-mail From: Gaucher Philippe Newsgroups: gmane.science.mathematics.categories Subject: Re: size_question Date: Wed, 29 Jun 2011 09:01:15 +0200 Message-ID: References: Reply-To: Gaucher Philippe NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: Text/Plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1309353906 25866 80.91.229.12 (29 Jun 2011 13:25:06 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 29 Jun 2011 13:25:06 +0000 (UTC) Cc: Categories To: Eduardo Dubuc Original-X-From: majordomo@mlist.mta.ca Wed Jun 29 15:25:00 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 1QbulH-00022P-K1 for gsmc-categories@m.gmane.org; Wed, 29 Jun 2011 15:24:59 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:44784) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1Qbujb-0002vI-CS; Wed, 29 Jun 2011 10:23:15 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1Qbuja-0002e4-Lv for categories-list@mlist.mta.ca; Wed, 29 Jun 2011 10:23:14 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6725 Archived-At: Le mardi 28 juin 2011 19:39:10, vous avez =E9crit : > This is a naive question on non naive foundations. >=20 > Consider the inclusion S_f C S of finite sets in sets. >=20 > Is the category S_f closed under finite limits and at the same time small= ? >=20 > For example, there are a proper class of singletons, all finite. Thus a > proper class of empty limits. This is the definition of quasi-small, not small: a set of isomorphism clas= ses=20 ? The category of finite sets is quasi-small, not small. And we need the ax= iom=20 of choice for that, as for many things in category theory.=20 pg. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]