Topological Galois theory
Copyright policy )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.
82 pages
- Paris Diderot University France
- Università dell Insubria (Varese) Italy
- University of Insubria Italy
ultrahomogeneous structure, Topoi, Galois theory, atomic and complete theory, automorphism group, Mathematics - Category Theory, Mathematics - Logic, Group Theory (math.GR), Mathematics - Algebraic Geometry, Galois category, 03G30, 18C10, 18B25, 03C13, 03C35, 13B05, 20B05, 14A99, FOS: Mathematics, atomic topos, Category Theory (math.CT), Atomic and complete theory; Atomic topos; Automorphism group; Galois category; Galois theory; Grothendieck topos; Ultrahomogeneous structure; Mathematics (all), Logic (math.LO), Mathematics - Group Theory, Algebraic Geometry (math.AG), Grothendieck topos, Categorical logic, topoi
ultrahomogeneous structure, Topoi, Galois theory, atomic and complete theory, automorphism group, Mathematics - Category Theory, Mathematics - Logic, Group Theory (math.GR), Mathematics - Algebraic Geometry, Galois category, 03G30, 18C10, 18B25, 03C13, 03C35, 13B05, 20B05, 14A99, FOS: Mathematics, atomic topos, Category Theory (math.CT), Atomic and complete theory; Atomic topos; Automorphism group; Galois category; Galois theory; Grothendieck topos; Ultrahomogeneous structure; Mathematics (all), Logic (math.LO), Mathematics - Group Theory, Algebraic Geometry (math.AG), Grothendieck topos, Categorical logic, topoi
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