Abstract
Let A be a commutative Hopf algebra over a field k; the k-valued fibre functors on the category of finite dimensional A-comodules correspond to Spec(A)-torsors over k as was shown by Saavedra Rivano and Deligne-Milne. We prove a non-commutative version of this result by using methods developed in a previous paper [5] for the case of finite Hopf algebras over a commutative ring. We also exhibit right adjoints for fibre functors under the assumption that the antipode is bijective.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
DELIGNE, P.: Catégories tannakiennes, preprint
DELIGNE, P., MILNE, J.: Tannakian Categories, Lecture Notes in Math. 900, Springer-Verlag 1982, pp. 101–228
MITCHELL, B.: Theory of Categories, Academic Press 1965
SAAVEDRA RIVANO, N.: Catégories Tannakiennes, Lecture Notes in Math. 265, Springer-Verlag 1972
ULBRICH, K.-H.: Galois extensions as functors of comodules, manuscripta math. 59, 391–397 (1987)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ulbrich, K.H. Fibre functors of finite dimensional comodules. Manuscripta Math 65, 39–46 (1989). https://doi.org/10.1007/BF01168365
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01168365