Cleft Comodule Categories

Abstract

We define crossed product categories and we show that they are equivalent with cleft comodule categories. We also prove that a comodule category is cleft if and only if it is Hopf–Galois and has a normal basis. As an application we show that the category of Hopf modules over a cleft linear category and the category of modules over the coinvariant subcategory are equivalent.

Key Words:

• Cleft linear category
• Hopf–Galois extension
• Linear categories
• Smash product

2010 Mathematics Subject Classification:

• Primary 18D20
• Secondary 16T05

ACKNOWLEDGMENTS

The first named author was financially supported by the funds of the Contract POSDRU/6/1.5/S/12. The second named author was financially supported by CNCSIS, Contract 560/2009 (CNCSIS code ID_69).

Notes

Communicated by T. Albu.