From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3839 Path: news.gmane.org!not-for-mail From: "Stephen Lack" Newsgroups: gmane.science.mathematics.categories Subject: Re: Bicomma objects Date: Wed, 25 Jul 2007 09:54:22 +1000 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019554 10531 80.91.229.2 (29 Apr 2009 15:39:14 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:39:14 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Wed Jul 25 09:38:28 2007 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Wed, 25 Jul 2007 09:38:28 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1IDg2v-0004c8-DT for categories-list@mta.ca; Wed, 25 Jul 2007 09:32:53 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 33 Original-Lines: 36 Xref: news.gmane.org gmane.science.mathematics.categories:3839 Archived-At: Dear Steve, A bicomma object is a bicategorical limit, so determined only up to equivalence. A comma object is a strict limit, so determined up to isomorphism.=20 In the case of Cat, comma objects are just the usual comma categories (strictly speaking, anything isomorphic to the comma category), while anything equivalent to the comma category will be a bicomma object. So any comma object is also a bicomma object, but the converse is false. Moreover, there are 2-categories in which bicomma objects exist but comma objects do not. The situation with pullbacks, by the way, is slightly different. It is not the case that every pullback is a bipullback (but there is a paper=20 of Joyal and Street giving a sufficient condition for a pullback to be a bipullback). Steve. -----Original Message----- From: cat-dist@mta.ca on behalf of Steve Vickers Sent: Wed 25/07/2007 2:02 AM To: categories@mta.ca Subject: categories: Bicomma objects =20 What is the difference between a bicomma object and a comma object (a.k.a. lax pullback)? Steve.