Topological Galois Theory

@article{Caramello2013TopologicalGT,
  title={Topological Galois Theory},
  author={Olivia Caramello},
  journal={arXiv: Category Theory},
  year={2013}
}
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. 
16 Citations
Some aspects of topological Galois theory
  • PDF
Motivic toposes
  • PDF
Azumaya toposes
  • 2
  • PDF
Fraïssé’s Construction from a Topos-Theoretic Perspective
  • 13
  • PDF
A topos-theoretic view of difference algebra
  • 3
  • PDF
Toposes of Discrete Monoid Actions
  • 4
  • PDF
Sites whose topoi are the smooth representations of locally profinite groups
  • Highly Influenced
  • PDF
On Supercompactly and Compactly Generated Toposes
  • PDF
...
1
2
...

References

SHOWING 1-10 OF 50 REFERENCES
Atomic Toposes and Countable Categoricity
  • 10
  • PDF
Fraïssé’s Construction from a Topos-Theoretic Perspective
  • 13
  • PDF
Strongly algebraic = SFP (topically)
  • S. Vickers
  • Mathematics, Computer Science
  • Mathematical Structures in Computer Science
  • 2001
  • 16
Classifying topoi and finite forcing
  • 21
  • PDF
Sketches of an Elephant: A Topos Theory Compendium Volume 1
  • 744
  • Highly Influential
On the representation theory of Galois and atomic topoi
  • 10
  • PDF
On the Galois Theory of Grothendieck
  • 12
  • PDF
The unification of Mathematics via Topos Theory
  • 36
  • PDF
SYNTACTIC CHARACTERIZATIONS OF PROPERTIES OF CLASSIFYING TOPOSES
  • 16
  • PDF
...
1
2
3
4
5
...