Tannakian formalism
In mathematics, a Tannakian category is a particular kind of monoidal category C, equipped with some extra structure relative to a given field K. The role of such categories C is to generalise the category of linear representations of an algebraic group G defined over K. A number of major applications of the theory have been made, or might be made in pursuit of some of the central conjectures of contemporary algebraic geometry and number theory. The name is taken from Tadao Tannaka and Tannaka–Krein duality, a theory about compact groups G and their representation theory.