From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6409 Path: news.gmane.org!not-for-mail From: Richard Garner Newsgroups: gmane.science.mathematics.categories Subject: Re: Terminology of locally small categories without replacement Date: Wed, 8 Dec 2010 09:22:08 +1100 Message-ID: References: Reply-To: Richard Garner NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1291776234 30502 80.91.229.12 (8 Dec 2010 02:43:54 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 8 Dec 2010 02:43:54 +0000 (UTC) Cc: JeanBenabou To: Categories mailing list Original-X-From: majordomo@mlist.mta.ca Wed Dec 08 03:43:49 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.114]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1PQA0T-0000D3-AW for gsmc-categories@m.gmane.org; Wed, 08 Dec 2010 03:43:49 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:42795) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PQA0B-00075j-Mh; Tue, 07 Dec 2010 22:43:31 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PQA08-0006lQ-8k for categories-list@mlist.mta.ca; Tue, 07 Dec 2010 22:43:28 -0400 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6409 Archived-At: Dear Jean, > Could you please tell me: > (i) Given a category S how does one chose the finitely complete 2- > category K and the class C of small objects so that the locally small > objects of K in your sense, are the locally small fibrations over S ? Take K = Fib(S) and take C to be the representable fibrations. For me this is actually the easiest way to remember the definition of locally small fibration. > (iii) What significant mathematical examples can you give of your > notion ? See (i). Best regards, Richard [For admin and other information see: http://www.mta.ca/~cat-dist/ ]