A Tannakian Context for Galois
Abstract
Strong similarities have been long observed between the Galois (Categories Galoisiennes) and the Tannaka (Categories Tannakiennes) theories of representation of groups. In this paper we construct an explicit (neutral) Tannakian context for the Galois theory of atomic topoi, and prove the equivalence between its fundamental theorems. Since the theorem is known for the Galois context, this yields, in particular, a proof of the fundamental (recognition) theorem for a new Tannakian context. This example is different from the additive cases or their generalization, where the theorem is known to hold, and where the unit of the tensor product is always an object of finite presentation, which is not the case in our context.
Keywords
Cite
@article{arxiv.1110.6411,
title = {A Tannakian Context for Galois},
author = {Eduardo J. Dubuc and Martin Szyld},
journal= {arXiv preprint arXiv:1110.6411},
year = {2015}
}
Comments
This is a revision. We switch some of the proofs to another level of abstraction. We generalized the equivalence between the Tannaka and the Galois recognition theorems from atomic to arbritrary topoi. We strengthened the result "The Tannaka lifting functor is an equivalence" for atomic topos to "The Tannaka lifting functor is an equivalence if and only if the topos is atomic"