From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6734 Path: news.gmane.org!not-for-mail From: "Eduardo J. Dubuc" Newsgroups: gmane.science.mathematics.categories Subject: size_question_reloaded Date: Sun, 03 Jul 2011 19:59:16 -0300 Message-ID: Reply-To: "Eduardo J. Dubuc" NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=windows-1252; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1309777477 451 80.91.229.12 (4 Jul 2011 11:04:37 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Mon, 4 Jul 2011 11:04:37 +0000 (UTC) To: Categories list Original-X-From: majordomo@mlist.mta.ca Mon Jul 04 13:04:33 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 1Qdgx5-0005FK-NW for gsmc-categories@m.gmane.org; Mon, 04 Jul 2011 13:04:31 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:33915) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QdgvK-0005Dv-Pd; Mon, 04 Jul 2011 08:02:42 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QdgvK-0008S4-4x for categories-list@mlist.mta.ca; Mon, 04 Jul 2011 08:02:42 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6734 Archived-At: Thanks to all who wrote something on this question. It clarified mi ignorance: There is the category of finite sets, namely, the category of all those=20 sets which happen to be finite. No need of more precision. But it is not=20 small (or an element of the universe if you like). If you want small, then there are plenty of them, and anybody can use=20 their FAVORITE one. But this is not usually done, it seems that the fact=20 that the canonical one is =93essentially small=94 is good enough to dismi= ss=20 all possible problems. For example, people which consider the presheaf category=20 Set^((Set_f)^op) (object classifier) often do as if Set_f were=20 canonical and small. Now, if you work with a Grothendieck base topos =93as if it were the=20 category of sets=94, you are forced to specify which small category of=20 finite sets you are using, or not ?. Cheers e.d. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]