We develop a theory of tensor categories over a field endowed with abstract operators. Our notion of a "field with operators", derived from the work of Moosa and Scanlon, includes the familiar cases of differential and difference fields, Hasse-Schmidt derivations, and their combinations. We develop a corresponding Tannakian formalism, describing the category of representations of linear groups defined over such fields. This paper extends the previously known (classical) algebraic and differential algebraic Tannakian formalisms.
ASJC Scopus subject areas
- Mathematics (all)