From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2571 Path: news.gmane.org!not-for-mail From: "Ronald Brown" Newsgroups: gmane.science.mathematics.categories Subject: Re: Who invented n-categories? Date: Wed, 25 Feb 2004 09:57:21 -0000 Message-ID: <02dc01c3fb87$d0074540$befd4c51@brown1> References: <159.2e745aaa.2d6b7dcf@aol.com> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241018754 4786 80.91.229.2 (29 Apr 2009 15:25:54 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:25:54 +0000 (UTC) To: Original-X-From: rrosebru@mta.ca Fri Feb 27 11:16:20 2004 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 27 Feb 2004 11:16:20 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 1Awjh1-0005CD-00 for categories-list@mta.ca; Fri, 27 Feb 2004 11:14:23 -0400 X-Priority: 3 X-MSMail-Priority: Normal X-Mailer: Microsoft Outlook Express 6.00.2800.1106 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 37 Original-Lines: 53 Xref: news.gmane.org gmane.science.mathematics.categories:2571 Archived-At: reply to r.brown@bangor.ac.uk There is the following paper 34. (with P.J. HIGGINS), ``The equivalence of $\infty$-groupoids and crossed complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981) 371-386. which first defines an n-fold category, specialises to an n-category, and relates that to a notion of globular set in (2.2), (2.3), (without using the term globular, which I think came from Pursuing Stacks, 1983). Published at the same time was 33. (with P.J. HIGGINS), ``The equivalence of $\omega$-groupoids and cubical $T$-complexes'', {\em Cah. Top. G\'eom. Diff.} 22 (1981) 349-370 which deals with the cubical, groupoid, case (essential for the topological applications) and of which some announcement was made in 22. (with P.J. HIGGINS), ``Sur les complexes crois\'es, $\omega$-groupo\"{\i}des et T-complexes'', {\em C.R. Acad. Sci. Paris S\'er. A.} 285 (1977) 997-999. Were there earlier definitions? There was an unpublished manuscript by O. Wyler (1972) referred to in 34, which my memory suggests did define n-fold categories. Ronnie Brown http://www.bangor.ac.uk/~mas010 ----- Original Message ----- From: To: Sent: Monday, February 23, 2004 4:01 PM Subject: categories: Who invented n-categories? > Can anyone offer a reference to the first published work which defined a > notion of strict n-category equivalent to that used today? > > I know that Ehresmann invented n-tuple ( or n-fold ) categories which > contain strict n-categories as special cases. If this is the first > implicit defintion of strict n-category does anyone know who was the first > to isolate our current notion of strict n-category as a particularly > interesting special case of an n-tuple category? > > Carl Futia >