From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5271 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: intersections of classes Date: Fri, 13 Nov 2009 14:15:52 -0800 Message-ID: References: Reply-To: Toby Bartels NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1258208708 30574 80.91.229.12 (14 Nov 2009 14:25:08 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 14 Nov 2009 14:25:08 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Sat Nov 14 15:25:02 2009 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.50) id 1N9JYi-0007Od-To for gsmc-categories@m.gmane.org; Sat, 14 Nov 2009 15:25:01 +0100 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1N9J2s-00043i-Rt for categories-list@mta.ca; Sat, 14 Nov 2009 09:52:06 -0400 Content-Disposition: inline Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5271 Archived-At: Andrew Salch wrote: >>let C be a class, and consider a family of subclasses C_i of C, which >>are indexed by an index class I. Am I allowed to take the intersection >>of a family of classes indexed by a class? Is the result a class? Mike Shulman's answer is more comprhensive than what I could write, but I want to stress two points. For the first point, I quote Mike: >I think you *can* still define this intersection in MK, however So there is a well-known theory of sets and classes in which you can do this. And the second point is that, unless you are particulary interested in the foundational and logical issues of size and categories, the first point is the only thing that you should care about. (Mike and I are interested in those issues, which is why he wrote a detailed answer and I was happy to read it. But "working" category theorists shouln't have to be.) --Toby [For admin and other information see: http://www.mta.ca/~cat-dist/ ]