From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1169 Path: news.gmane.org!not-for-mail From: cxm7@po.cwru.edu (Colin McLarty) Newsgroups: gmane.science.mathematics.categories Subject: RE: Mac Lane's inclusions Date: Mon, 19 Jul 1999 15:45:29 -0400 (EDT) Message-ID: <199907191945.PAA22541@babar.INS.CWRU.Edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" X-Trace: ger.gmane.org 1241017612 29797 80.91.229.2 (29 Apr 2009 15:06:52 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:06:52 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Tue Jul 20 09:00:27 1999 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id HAA29969 for categories-list; Tue, 20 Jul 1999 07:22:10 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: cxm7@pop.cwru.edu X-Mailer: Windows Eudora Version 1.4.4 Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 21 Xref: news.gmane.org gmane.science.mathematics.categories:1169 Archived-At: Robert W. McGrail wrote: >Correct me if I am wrong, but it seems to me that every \tau-category is a >category with inclusions. Moreover, I recall a result by Freyd that every >(sufficiently small? cartesian?) category is equivalent to a \tau-category. > The proof does not use choice. There is certainly a similarity. Tau categories are cartesian categories (categories with all finite limits) which not only have selected monics but also selected jointly-monic n-tuples for all finite n; and all these things compose. Freyd shows every cartesian category is equivalent to a tau category. My construction seems very like Peter's but shortened by working only on monics and not jointly monic lists, and never using limits. best, Colin