From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4469 Path: news.gmane.org!not-for-mail From: Michael Fourman Newsgroups: gmane.science.mathematics.categories Subject: Re: Paper on slice stability in Locale Theory Date: Fri, 8 Aug 2008 21:40:33 +0100 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v926) Content-Type: text/plain; charset=US-ASCII; format=flowed; delsp=yes Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019966 13454 80.91.229.2 (29 Apr 2009 15:46:06 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:46:06 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Fri Aug 8 20:53:13 2008 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 08 Aug 2008 20:53:13 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1KRbjb-00067m-BO for categories-list@mta.ca; Fri, 08 Aug 2008 20:51:03 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 4 Original-Lines: 58 Xref: news.gmane.org gmane.science.mathematics.categories:4469 Archived-At: The result was in the air - and I'm sure that Joyal in particular saw it clearly. For me it (or at least the logical version of it given in Fourman- Scott) came as an answer to Dana's request for a description of an internal cHa in a category of "Omega sets". I don't think I had already heard it from Joyal - but I'm sure he already knew it. It was easy to see that an object of Loc/Omega represented an internal cHa, by generalisation of the representation of examples such as the internal cHa O(R) in Sh(X) as O(RxX) -> O(X), or relaxation of the representation of sheaves by local homeomorphisms. Our paper was deliberately (and perhaps mistakenly) concrete rather than abstract, so we didn't think to phrase the representation explicitly as an equivalence of categories. A related (but even more logical and obstinately pointed) result is given in Michael P. Fourman. T1 spaces over topological sites. J. Pure and Applied Algebra, 27(3):223-224, March 1983. On 6 Aug 2008, at 16:00, Prof. Peter Johnstone wrote: > On Thu, 31 Jul 2008, Townsend, Christopher wrote: > >> Feedback is welcome. For example, I have always attributed the result >> Loc/Y =3D Loc_Sh(Y) to Joyal and Tierney. Am I right?=20 >> > I think it predates the Joyal--Tierney work by a couple of years. > It's (more or less) present in the long Fourman--Scott paper on > sheaves and logic in SLN 753 (the Proceedings of the 1977 Durham > symposium), but they don't claim originality for it. > > Peter Johnstone > > > > _______________________________________________ > categories mailing list > categories@inf.ed.ac.uk > http://lists.inf.ed.ac.uk/mailman/listinfo/categories > > Professor Michael Fourman FBCS CITP Head of Informatics University of Edinburgh Informatics Forum 10 Crichton Street Edinburgh EH8 9AB Tel: +44 131 650 2690 michael.fourmaned.ac.uk