On 1/3/2013 8:34 PM, meekerdb wrote:
On 1/3/2013 5:06 PM, Stephen P. King wrote:
Hi Bruno,

    You might be interested in this!

How about giving us a 500 word summary including an example of it's application.
Hi Brent,

I guess that you can't be bothered to read it for yourself. OK, but why advertize the fact? I guess you don't understand category theoretical stuff... OK. Section 6.3 and 6.4 are very nice formal treatments of the idea that I am exploring, the Stone duality thing that I am often sputtering on and on about. ;-) My idea is that Boolean algebras can evolve via non-exact homomorphsims. ;-) I just don't happen to think or write in formal terms.


-------- Original Message --------
Subject:        [FOM] Preprint: "Topological Galois Theory"
Date:   Thu, 3 Jan 2013 20:08:04 +0100
From:   Olivia Caramello <oc...@hermes.cam.ac.uk>
Reply-To:       Foundations of Mathematics <f...@cs.nyu.edu>
To:     Foundations of Mathematics <f...@cs.nyu.edu>

Dear All,

The following preprint is available from the Mathematics ArXiv at the
addresshttp://arxiv.org/abs/1301.0300  :

O. Caramello, "Topological Galois Theory"


We introduce an abstract topos-theoretic framework for building Galois-type
theories in a variety of different mathematical contexts; such theories are
obtained from representations of certain atomic two-valued toposes as
toposes of continuous actions of a topological group. Our framework subsumes
in particular Grothendieck's Galois theory and allows to build Galois-type
equivalences in new contexts, such as for example graph theory and finite
group theory.

This work represents a concrete implementation of the abstract methodologies
introduced in the paper "The unification of Mathematics via Topos Theory",
which was advertised on this list two years ago. Other recent papers of mine
applying the same general principles in other fields are available for
download at the addresshttp://www.oliviacaramello.com/Papers/Papers.htm  .
Best wishes for 2013,

Olivia Caramello



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