From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2484 Path: news.gmane.org!not-for-mail From: "John Baez" Newsgroups: gmane.science.mathematics.categories Subject: regular, geometric, and coherent categories Date: Fri, 24 Oct 2003 18:08:47 -0700 (PDT) Message-ID: <200310250108.h9P18lo20637@math-cl-n01.ucr.edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018698 4370 80.91.229.2 (29 Apr 2009 15:24:58 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:24:58 +0000 (UTC) To: categories@mta.ca (categories) Original-X-From: rrosebru@mta.ca Sat Oct 25 08:48:39 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sat, 25 Oct 2003 08:48:39 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1ADMoU-0001tX-00 for categories-list@mta.ca; Sat, 25 Oct 2003 08:42:34 -0300 X-Mailer: ELM [version 2.5 PL6] Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 35 Original-Lines: 28 Xref: news.gmane.org gmane.science.mathematics.categories:2484 Archived-At: I wrote: > Here's some stuff I think I know. I know the definitions of > the above concepts, as long as I have the book open to the > right page... but I left it at home, so these could be wrong! Some were. > Cartesian categories have finite limits. Regular categories > are cartesian categories with regular epi/mono factorizations, > which must be stable under pullbacks. Fine. > Geometric categories are > regular categories admitting arbitrary unions of subobjects, > which must be stable under pullbacks. Coherent categories > are geometric categories where pullback of subobjects has a > right adjoint (which plays the role of "for all"). These were mixed up.