The Tannaka–Krein Formalism and (Re)Presentations of Universal Quantum Groups

Abstract

This is a draft version for an extra chapter in the second edition of the book "Quantum Groups and Noncommutative Geometry" by Yu. I. Manin [24]. We survey our work in [28,29, 30], placing particular emphasis on the Tannaka-Krein formalism.is the unique C-linear exact faithful symmetric monoidal functor from rep C (G) to vect C , where vect C is the category of finite-dimensional C-vector spaces. Hence, we can assume F is known, and the following proposition then allows one to reconstruct G.Proposition 2.