From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1949 Path: news.gmane.org!not-for-mail From: Ross Street Newsgroups: gmane.science.mathematics.categories Subject: Re: Limits Date: Sun, 6 May 2001 10:26:04 +1000 Message-ID: References: <200105042104.f44L4al17252@math-cl-n03.ucr.edu> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" ; format="flowed" X-Trace: ger.gmane.org 1241018226 1357 80.91.229.2 (29 Apr 2009 15:17:06 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:17:06 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sun May 6 09:25:28 2001 -0300 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id f46Bqjb14218 for categories-list; Sun, 6 May 2001 08:52:45 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: street@hera.mpce.mq.edu.au In-Reply-To: <200105042104.f44L4al17252@math-cl-n03.ucr.edu> Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 17 Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:1949 Archived-At: I very much agree with James Dolan's response to the question of comparing categorical limits and adjoint functors with their abstract counterparts in analysis. Other words that have been used for "objectification" and "categorification" are "laxification" and "identity breaking". The original questions were a bit like asking: "Is the plus in an abelian group a categorical coproduct?" Lots of abelian groups can arise by taking isomorphism classes and using a categorical coproduct: but then we lose the beautiful universal property. Along the same lines, I enjoy bicategories, with coproducts in their homcategories (preserved by composition), much more than additive categories. Not only is every global coproduct in such a bicategory also a global product, but the projections from the global products are right adjoint to the coprojections into the coproduct. Ross