From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9484 Path: news.gmane.org!.POSTED!not-for-mail From: Eduardo Julio Dubuc Newsgroups: gmane.science.mathematics.categories Subject: Re: V-included categories Date: Mon, 1 Jan 2018 18:14:20 -0300 Message-ID: References: Reply-To: Eduardo Julio Dubuc NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit X-Trace: blaine.gmane.org 1514899811 13372 195.159.176.226 (2 Jan 2018 13:30:11 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Tue, 2 Jan 2018 13:30:11 +0000 (UTC) To: Paul Blain Levy , "Categories list\" " Original-X-From: majordomo@mlist.mta.ca Tue Jan 02 14:30:07 2018 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp2.mta.ca ([198.164.44.40]) by blaine.gmane.org with esmtp (Exim 4.84_2) (envelope-from ) id 1eWMdj-0002jA-Vu for gsmc-categories@m.gmane.org; Tue, 02 Jan 2018 14:30:00 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:45879) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1eWMga-0006hc-VL; Tue, 02 Jan 2018 09:32:56 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1eWMfC-00084s-6W for categories-list@mlist.mta.ca; Tue, 02 Jan 2018 09:31:30 -0400 In-Reply-To: Content-Language: es-ES Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9484 Archived-At: Have you considered the following at the very begining of SGA4: Remarque 1.1.2. ??? Soit D une cat??gorie poss??dant les propri??t??s suivantes : (C1) L???ensemble ob(D) est contenu dans l???univers U . (C2) Pour tout couple (x, y) d???objets de D, l???ensemble HomD(x, y) est un ??l??ment de U . (Les cat??gories usuelles construites ?? partir d???un univers U poss??dent ces deux propri??t??s: U -Ens, U -Ab,. . .). Soit C une cat??gorie appartenant ?? U . Alors la cat??gorie Fonct(C, D) ne poss??de pas en g??n??ral les propri??t??s (C1) et (C2). Par exemple la cat??gorie Fonct(C,U-Ens) ne poss??de aucune des propri??t??s (C1) et (C2). C???est ce qui justifie la d??finition adopt??e de U-cat??gorie, de pr??f??rence ?? la notion plus restrictive par les conditions (C1) et (C2) ci-dessus. best e.d. El 1/1/18 a las 10:10, Paul Blain Levy escribi??: > > Hi, > > Let V be a Grothendieck universe.?? A "V-set" is an element of V, and a > "V-class" is a subset of V. > > Say that a category C is "V-included" when it has the following two > properties. > > (1) ob C is a V-class. > > (2) C(x,y) is a V-set for all x,y in ob C. > > The advantage of V-inclusion over local V-smallness (i.e. condition (2) > alone) is that V-included categories are W-small for every universe W > greater than V, whereas locally V-small categories are not, in general. > > Furthermore, all the standard categories constructed from V are > V-included.?? (Except for the ones that are not even locally V-small, > like the category of V-included categories.) > > Is there a standard name for V-inclusion? > > Paul > > > > > > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]