# Tannakian categories in positive characteristic

## TL;DR

This paper characterizes when tensor categories over fields of positive characteristic are (super) tannakian, extending Deligne's characteristic zero results, and investigates Frobenius twists in such categories.

## Contribution

It provides internal criteria for (super) tannakian categories in positive characteristic and explores Frobenius twists, generalizing known results from characteristic zero.

## Key findings

- Characterizations for (super) tannakian categories in positive characteristic
- Extension of Deligne's criteria to positive characteristic
- Analysis of Frobenius twists in tensor categories

## Abstract

We determine internal characterisations for when a tensor category is (super) tannakian, for fields of positive characteristic. This generalises the corresponding characterisations in characteristic zero by P. Deligne. We also explore notions of Frobenius twists in tensor categories in positive characteristic.