On hopf algebras and rigid monoidal categories

LetC be a neutral Tannakian category over a fieldk. By a theorem of Saavedra Rivano there exists a commutative Hopf algebraA overk such thatC is equivalent to the category of finite dimensional rightA-comodules. We review Saavedra Rivano’s construction of the bialgebraA and show thatA has still an antipode if the symmetry condition on the monoidal structure ofC is removed.