From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1731 Path: news.gmane.org!not-for-mail From: "Robert J. MacG. Dawson" Newsgroups: gmane.science.mathematics.categories Subject: Re: Categories ridiculously abstract Date: Sat, 02 Dec 2000 09:34:22 -0400 Message-ID: <3A28FA5E.9640F981@stmarys.ca> References: 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 1241018051 32638 80.91.229.2 (29 Apr 2009 15:14:11 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:14:11 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sat Dec 2 11:07:17 2000 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id eB2EOTw26183 for categories-list; Sat, 2 Dec 2000 10:24:29 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: Mozilla 4.72 [en] (WinNT; I) X-Accept-Language: en Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 4 Original-Lines: 30 Xref: news.gmane.org gmane.science.mathematics.categories:1731 Archived-At: Tom Leinster wrote: > > Michael Barr wrote: > > > > And here is a question: are categories more abstract or less abstract than > > sets? > > A higher-dimensional category theorist's answer: > "Neither - a set is merely a 0-category, and a category a 1-category." > > There's a more serious thought behind this. Sometimes I've wondered, in a > vague way, whether the much-discussed hierarchy > > 0-categories (sets) form a (1-)category, > (1-)categories form a 2-category, > ... > > has a role to play in foundations. After all, set-theorists seek to found > mathematics on the theory of 0-categories; category-theorists sometimes talk > about founding mathematics on the theory of 1-categories and providing a > (Lawverian) axiomatization of the 1-category of 0-categories; you might ask > "what next"? Axiomatize the 2-category of (1-)categories? Or the > (n+1)-category of n-categories? Surely we should start with the set of (-1)-categories? -Robert Dawson