From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/935 Path: news.gmane.org!not-for-mail From: "Martin Escardo" Newsgroups: gmane.science.mathematics.categories Subject: preprint available Date: Wed, 18 Nov 1998 16:09:09 +0000 (GMT) Message-ID: <13906.60796.497804.182184@mhuilinn.dcs.ed.ac.uk> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit X-Trace: ger.gmane.org 1241017350 28389 80.91.229.2 (29 Apr 2009 15:02:30 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:02:30 +0000 (UTC) To: categories@mta.ca Original-X-From: cat-dist Wed Nov 18 15:36:38 1998 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id OAA20916 for categories-list; Wed, 18 Nov 1998 14:07:57 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Mailer: VM 6.43 under 20.4 "Emerald" XEmacs Lucid X-MIME-Autoconverted: from quoted-printable to 8bit by mailserv.mta.ca id MAA30554 Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:935 Archived-At: The following preprint is available at http://www.dcs.ed.ac.uk/home/mhe/pub/papers/patch-CSLC.ps.gz & http://www.dcs.ed.ac.uk/home/mhe/papers.html & ftp://ftp.dcs.ed.ac.uk/pub/mhe/patch-CSLC.ps.gz On the compact-regular coreflection of a compact stably locally compact locale. ABSTRACT: The Scott continuous nuclei form a subframe of the frame of all nuclei. We refer to this subframe as the patch frame. We show that the patch construction exhibits (i) the category of Stone locales and continuous maps as a coreflective subcategory of the category of coherent locales and coherent maps, (ii) the category of compact regular locales and continuous maps as a coreflective subcategory of the category of compact stably locally compact locales and perfect maps, and (iii) the category of regular locally compact locales and continuous maps as a coreflective subcategory of the category of stably locally compact locales. We relate our patch construction to Banaschewski and Brümmer's construction of the dual equivalence of the category of compact stably locally compact locales and perfect maps with the category of compact regular biframes and biframe homomorphisms. Comments are welcome. ----------------------------------------------------------------- Martin H. Escardo, LFCS, Computer Science, Edinburgh University King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, Scotland office: 2606 (JMCB) fax: +44 131 667 7209 phone: +44 131 650 5135 mailto:mhe@dcs.ed.ac.uk http://www.dcs.ed.ac.uk/home/mhe -----------------------------------------------------------------