TL;DR
This paper introduces differential Tannakian categories, proves their equivalence to categories of representations of differential algebraic groups under certain conditions, using differential Hopf algebras and Deligne's fibre functor.
Contribution
It defines differential Tannakian categories and establishes their equivalence to differential algebraic group representations with a new approach involving differential Hopf algebras.
Findings
Differential Tannakian categories can have a fibre functor under natural assumptions.
Neutral differential Tannakian categories are equivalent to representations of differential algebraic groups.
The approach uses differential Hopf algebras and Deligne's fibre functor construction.
Abstract
We define a differential Tannakian category and show that under a natural assumption it has a fibre functor. If in addition this category is neutral, that is, the target category for the fibre functor are finite dimensional vector spaces over the base field, then it is equivalent to the category of representations of a (pro-)linear differential algebraic group. Our treatment of the problem is via differential Hopf algebras and Deligne's fibre functor construction.
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