From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1444 Path: news.gmane.org!not-for-mail From: Paul Taylor Newsgroups: gmane.science.mathematics.categories Subject: gluing, lifting and partial maps Date: Wed, 15 Mar 2000 13:11:31 GMT Message-ID: <200003151311.NAA15811@koi-pc.dcs.qmw.ac.uk> NNTP-Posting-Host: main.gmane.org X-Trace: ger.gmane.org 1241017835 31291 80.91.229.2 (29 Apr 2009 15:10:35 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:10:35 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Mar 15 14:19:06 2000 -0400 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id JAA13309 for categories-list; Wed, 15 Mar 2000 09:39:06 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:1444 Archived-At: I have long regarded it as "well known" that the partial map classifier for topological spaces or locales where by "partial" I mean a continuous function defined on an open subset is the Artin gluing, Freyd cover or scone (Sierpinski cone). Can anybody point me to a published proof of this, or even tell me who first proved it? The same construction, with frames replaced by the categories of contexts and substitutions (a.k.a. classifying categories) for theories in other fragments of logic, has also been used with spectacular results to prove consistency, strong normalisation, etc. I know of plenty of work on that application itself, but I wonder whether anybody has investigated the connection between these two applications of the construction. Paul PS Thanks to everyone who wrote to me about 1970s calculators. I will be writing back and summarising the responses for "categories" after the end of term. When the students have sat my exam paper (sometime in May) I will also post to "categories" the actual question that I composed.