From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1726 Path: news.gmane.org!not-for-mail From: Tom Leinster Newsgroups: gmane.science.mathematics.categories Subject: Re: Categories ridiculously abstract Date: Thu, 30 Nov 2000 17:30:30 +0000 (GMT) Message-ID: 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 1241018048 32622 80.91.229.2 (29 Apr 2009 15:14:08 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:14:08 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Dec 1 15:15:23 2000 -0400 Return-Path: Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.11.1/8.11.1) id eB1IUCn13727 for categories-list; Fri, 1 Dec 2000 14:30:12 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: ELM [version 2.5 PL3] Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 57 Original-Lines: 28 Xref: news.gmane.org gmane.science.mathematics.categories:1726 Archived-At: 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? Could it even be, I ask with tongue in cheek and head in clouds, that general n-categories provide a more natural foundation than either 0-categories or 1-categories? Tom