From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3039 Path: news.gmane.org!not-for-mail From: Andrej Bauer Newsgroups: gmane.science.mathematics.categories Subject: Re: Voevodsky on the homotopy lambda calculus Date: Thu, 23 Feb 2006 23:24:49 +0100 Message-ID: <200602232324.50115.Andrej.Bauer@andrej.com> References: 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 1241019059 6990 80.91.229.2 (29 Apr 2009 15:30:59 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:30:59 +0000 (UTC) To: categories Original-X-From: rrosebru@mta.ca Fri Feb 24 19:56:34 2006 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 24 Feb 2006 19:56:34 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FCmgV-0000LZ-Jo for categories-list@mta.ca; Fri, 24 Feb 2006 19:49:15 -0400 User-Agent: KMail/1.8.3 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 22 Original-Lines: 22 Xref: news.gmane.org gmane.science.mathematics.categories:3039 Archived-At: On Wednesday 22 February 2006 22:53, John Baez wrote: > From an n-categorical > viewpoint it's natural to avoid working with equivalence classes > and instead use 2-morphisms between morphisms, like associators, > and so on, thus getting a "weak cartesian closed omega-category" - > a concept which, alas, has probably not been defined yet. I don't know about the omega-wheel, but at least the 2-wheel needs not be reinvented. For "cartesian closed 2-categories", a relevant reference is R.A.G. Seely, "Modelling computations: A 2-categorical framework". In Proceedings of the Second Symposium on Logic in Computer Science, pages 61--71, IEEE Computer Science Press, June 1987. I believe the above paper is "the first" on this topic (am I wrong?), and there must be more recent work. I know Neil Ghani did some, but Google also knows about "2-Lambda Calculus" by David Rydeheard, see http://www.cs.man.ac.uk/~david/publications/TwoLambdaCalculus.ps . Andrej