## Abstract

Descent theory for linear categories is developed. Given a linear category as an extension of a diagonal category, we introduce descent data, and the category of descent data is isomorphic to the category of representations of the diagonal category, if some flatness assumptions are satisfied. Then Hopf-Galois descent theory for linear Hopf categories, the Hopf algebra version of a linear category, is developed. This leads to the notion of Hopf-Galois category extension. We have a dual theory, where actions by dual linear Hopf categories on linear categories are considered. Hopf-Galois category extensions over groupoid algebras correspond to strongly graded linear categories.

Original language | English |
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Article number | 1850120 |

Number of pages | 39 |

Journal | Journal of Algebra and Its Applications |

Volume | 17 |

Issue number | 7 |

DOIs | |

Publication status | Published - 1 Jul 2018 |

## Keywords

- descent theory
- Enriched category
- Hopf category
- Hopf-Galois extension