From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6393 Path: news.gmane.org!not-for-mail From: Colin McLarty Newsgroups: gmane.science.mathematics.categories Subject: Terminology of locally small categories without replacement Date: Wed, 1 Dec 2010 17:00:51 -0500 Message-ID: Reply-To: Colin McLarty NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1 X-Trace: dough.gmane.org 1291252267 22003 80.91.229.12 (2 Dec 2010 01:11:07 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Thu, 2 Dec 2010 01:11:07 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Thu Dec 02 02:10:58 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 1PNxhI-00046V-JU for gsmc-categories@m.gmane.org; Thu, 02 Dec 2010 02:10:56 +0100 Original-Received: from mlist.mta.ca ([138.73.1.63]:36555) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1PNxgo-0001cE-DT; Wed, 01 Dec 2010 21:10:26 -0400 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1PNxgk-0002Ex-JK for categories-list@mlist.mta.ca; Wed, 01 Dec 2010 21:10:22 -0400 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6393 Archived-At: Locally small categories are always defined as categories such that: LS) for any objects A,B there is a set of all arrows A-->B. When the base set theory includes the axiom scheme of replacement that is equivalent to a prima facie stronger property: ??) for any set of objects there is a set of all arrows between them. These two are not equivalent in the absence of the axiom scheme of replacement. There the second is much stronger, but it remains important. Is there a good term for it? thanks, Colin [For admin and other information see: http://www.mta.ca/~cat-dist/ ]