Tannakian Categories

The set of irreducible unitary representations of a locally compact (Hausdorff) commuative group itself forms a group under tensor products, a result known as Pontryagin duality. Tannakian categories provide a more general setting to talk about duals of topological groups. In particular, the category of finite dimensional representations of an affine group scheme is a neutral Tannakian category and all neutral Tannakian categories arise this way.