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 Tannakian context for Galois theory, and prove the equivalence between its fundamental theorems. Since the theorem is known for the Galois context, this brings, in particular, a proof of the fundamental (recognition) theorem for a Tannakian context different than the known additive cases, or their generalizations, where it is assumed that the unit of the tensor product is an object of finite presentation (that is, filtered colimits in the tensor category are constructed as in the category of sets).