From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/9480 Path: news.gmane.org!.POSTED!not-for-mail From: Paul Blain Levy Newsgroups: gmane.science.mathematics.categories Subject: V-included categories Date: Mon, 1 Jan 2018 13:10:38 +0000 Message-ID: Reply-To: Paul Blain Levy NNTP-Posting-Host: blaine.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit X-Trace: blaine.gmane.org 1514828942 13730 195.159.176.226 (1 Jan 2018 17:49:02 GMT) X-Complaints-To: usenet@blaine.gmane.org NNTP-Posting-Date: Mon, 1 Jan 2018 17:49:02 +0000 (UTC) User-Agent: Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Thunderbird/52.5.0 To: "Categories list\" " Original-X-From: majordomo@mlist.mta.ca Mon Jan 01 18:48:57 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 1eW4Ci-0002mo-4w for gsmc-categories@m.gmane.org; Mon, 01 Jan 2018 18:48:52 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:45736) by smtp2.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1eW4F2-0002OS-Gz; Mon, 01 Jan 2018 13:51:16 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1eW4Dd-0003rd-K8 for categories-list@mlist.mta.ca; Mon, 01 Jan 2018 13:49:49 -0400 Content-Language: en-US Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:9480 Archived-At: 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/ ]