From: Paul Taylor <pt@dcs.qmw.ac.uk>
To: categories@mta.ca
Subject: gluing, lifting and partial maps
Date: Wed, 15 Mar 2000 13:11:31 GMT [thread overview]
Message-ID: <200003151311.NAA15811@koi-pc.dcs.qmw.ac.uk> (raw)
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.
next reply other threads:[~2000-03-15 13:11 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
2000-03-15 13:11 Paul Taylor [this message]
2000-03-15 17:26 ` Ronnie Brown
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