On 04 Jan 2013, at 02:34, 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.
Good point. It is not uninteresting, but is very technical, and as a
foundation of math can be used for many things.
Grothendieck's Galois theory would need a 50h course before we can say
sensible things.
I use much simpler math, but most people have already difficulties.
Bruno
Brent
-------- 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
address http://arxiv.org/abs/1301.0300 :
O. Caramello, "Topological Galois Theory"
Abstract:
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 address http://www.oliviacaramello.com/Papers/Papers.htm
.
Best wishes for 2013,
Olivia Caramello
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