From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4480 Path: news.gmane.org!not-for-mail From: Newsgroups: gmane.science.mathematics.categories Subject: KT Chen's smooth CCC, a correction Date: Sun, 17 Aug 2008 15:07:56 -0400 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="utf-8" Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241019972 13499 80.91.229.2 (29 Apr 2009 15:46:12 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:46:12 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sun Aug 17 17:30:57 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Sun, 17 Aug 2008 17:30:57 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KUosB-0007ip-7X for categories-list@mta.ca; Sun, 17 Aug 2008 17:29:11 -0300 Content-Disposition: inline Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 15 Original-Lines: 36 Xref: news.gmane.org gmane.science.mathematics.categories:4480 Archived-At: 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=20 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,=20 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=20 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=20 special use of convex models for plots. Bill Lawvere