From: Ronnie Brown <r.brown@bangor.ac.uk>
To: categories@mta.ca
Subject: Re: gluing, lifting and partial maps
Date: Wed, 15 Mar 2000 17:26:34 +0000 [thread overview]
Message-ID: <38CFC7CA.6F3029CD@bangor.ac.uk> (raw)
In-Reply-To: <200003151311.NAA15811@koi-pc.dcs.qmw.ac.uk>
Abd-Allah and I dealt with this in
``A compact-open topology on partial maps with open domain'', {\em J. London
Math Soc.} (2) 21 (1980) 480-486.
as a development of work with Peter Booth in
``Spaces of partial maps, fibred mapping spaces and the compact-open
topology'', {\em Gen. Top. Appl.} 8 (1978) 181-195.
We got the idea of representability of partial maps from Peter Freyd's
article on topos theory. Is there an earlier result on these lines?
Ideas on making spaces over B into a Cartesian closed category came initially
from a paper of Rene Thom, and were developed in Peter's work at Hull. This
eventually suggested the topologisation of spaces of partial maps as a step
towards Top/B.
Ronnie Brown
Paul Taylor wrote:
> 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.
prev parent reply other threads:[~2000-03-15 17:26 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2000-03-15 13:11 Paul Taylor
2000-03-15 17:26 ` Ronnie Brown [this message]
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