[FOM] Preprint: "Topological Galois Theory"

Olivia Caramello oc233 at hermes.cam.ac.uk
Thu Jan 3 14:08:04 EST 2013

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"


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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