From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1422 Path: news.gmane.org!not-for-mail From: Ellis Cooper Newsgroups: gmane.science.mathematics.categories Subject: The Category of all Smooth Manifolds a la Lawvere Date: Fri, 18 Feb 2000 17:09:51 -0500 Message-ID: <821.100947405462$1241017821@news.gmane.org> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" X-Trace: ger.gmane.org 1241017821 31182 80.91.229.2 (29 Apr 2009 15:10:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:10:21 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Sat Feb 19 14:44:23 2000 -0400 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id NAA00344 for categories-list; Sat, 19 Feb 2000 13:40:01 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: ecooper@pop.iis.varian.com X-Mailer: QUALCOMM Windows Eudora Pro Version 4.0.2 Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 26 Xref: news.gmane.org gmane.science.mathematics.categories:1422 Archived-At: Hello, In his paper "Qualitative distinctions between some toposes of generalized graphs" (Contemporary Mathematics Volume 92, 1989, pp. 261-299) Lawvere mentions a "powerful theorem" that "justifies bypassing the complicated considerations" usually associated with defining a smooth manifold (charts, atlases, etc.). This is in the context of something called "closed under splitting of idempotents" and the kind of idempotent he is talking about, I think, is what you get if you embed a manifold in a sufficiently high-dimensional space, wrap it inside and out with foam, call that foamy thing an open set, and then the idempotent is the projection of the foam back onto the embedded manifold. What I would like is a carefully written, fully spelled out statement and proof of his theorem. Please advise. In fact, I would be even more delighted by a more standard (motivation, definition, theorem, proof) version of his entire paper, but I suppose that is too much to ask. Please reply directly to me, at Ellis D. Cooper Senior Software Engineer Varian Semiconductor Equipment Associates, Inc. ellis.cooper@vsea.com