A Tannakian context for Galois theory

AbstractStrong similarities have been long observed between the Galois and Tannaka theories of the representation of groups. In this paper we construct an explicit (neutral) Tannakian context for the Galois theory of atomic topoi and prove equivalence for the fundamental theorem. Since the theorem is known for the Galois context, this yields a proof of the fundamental (recognition) theorem for a new Tannakian context. This example is different from the additive cases or their generalization for which the theorem is known to hold and for which the unit of the tensor product is always an object of finite presentation, which is not the case in our context