categories: Abstract Stone Duality - manifesto and draft paper

[Paul Taylor <pt@dcs.qmw.ac.uk>]

	http://www.dcs.qmul.ac.uk/~pt/ASD/

I have now written a 7-page "manifesto" that gives a non-technical
introduction to the ideas behind Abstract Stone Duality, summarises
the four (draft or published) papers that I have written so far,
and describes the directions for further work.

In particular,
	"Subspaces in Abstract Stone Duality"
is the successor to
	"Sober Spaces and Continuations",
which I advertised on 1 September.

It shows how any category with an exponentiable object Sigma can be
completed to one in which the adjunction Sigma^(-) -| Sigma^(-) is monadic.
This is done in three ways: using the algebras directly,  by formally
adjoining Sigma-split equalisers, and by extending the lambda-calculus
with an "axiom of comprehension".   This last, and the normalisation
theorem that erases the subtype information, is what I presented at
the APPSEM workshop in Darmstadt in March.   However, although the
mathematical details are more or less all present, the paper is a long
way from being finished.

As usual, all comments are welcome.

Paul