From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4481 Path: news.gmane.org!not-for-mail From: jim stasheff Newsgroups: gmane.science.mathematics.categories Subject: Re: KT Chen's smooth CCC, a correction Date: Sun, 17 Aug 2008 17:51:12 -0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019973 13505 80.91.229.2 (29 Apr 2009 15:46:13 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:46:13 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Aug 18 09:26:08 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 18 Aug 2008 09:26:08 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KV3mX-00060e-4Y for categories-list@mta.ca; Mon, 18 Aug 2008 09:24:21 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 16 Original-Lines: 54 Xref: news.gmane.org gmane.science.mathematics.categories:4481 Archived-At: Bill, Happy to see you contributing to the renaissance in interest in Chen's work. It would be good to post your msg to the n-category cafe blog whee there's been an intense discussion of `smooth spaces' i various incarnaitons. jim http://golem.ph.utexas.edu/category/2008/05/convenient_categories_of_smoot.html wlawvere@buffalo.edu wrote: > In my review of Anders Kock's Synthetic > Differential Geometry, Second Edition, > there is a wrong statement that I want to correct. > (This was in the SIAM REVIEW, vol. 49, No.2 > pp 349-350). The statement was that Chen's > category does not include the representability > of smooth function spaces. But from his paper > In Springer Lecture Notes in Mathematics,vol > 1174, pp 38-42 it is clear that it does. I thank Anders > for pointing out this slip. > > This is a good opportunity to emphasize that > the works of KT Chen and of Alfred Frolicher > (that were referred to in the beginning of the > above review) contain several contributions > of value both to applications and to more > topos-theoretic formulations. For example, > Frolicher's use of Lemmas by Boman and others > reveals how little of the specific parameter "smooth" > needs to be given to the very general machinery of > adjoint functors and abstact sets in order to obtain > smooth infinite dimensional spaces of all kinds. > (Namely a suitable topos of actions by only unary > operations on the line is fully embedded > in the desired topos in such a way that the algebraic > theory of n-ary operations that naturally exist in > the small one determines the whole algebraic category whose > sheaves include the large one.) > And Chen's smooth space of piecewise-smooth > curves can surely be further applied, as can his > special use of convex models for plots. > > Bill Lawvere > > > >