Compact quantum groups associated with monoidal functors

Abstract

We provide a C ∗ {C}^\ast -algebra structure on the bialgebra associated with a monoidal linear ∗ {}^\ast -functor. The C ∗ {C}^\ast -algebra obtained in this way is a compact quantum group in the sense of Baaj and Skandalis. We show that the category of finite dimensional unitary corepresentations of this C ∗ {C}^\ast -algebra is equivalent to the given category.