Quantum group constructions in a symmetric monoidal category

Let H be a cotriangular Hopf algebra with a symmetric braiding. Using the twist given by the symmetric braiding rather than the usual flip for tensor products ive prove that both Manin's construction for quadratic algebras end(H)(A), and the FRT construction A(H)(R) can be done in the category of left H-comodules and give the same bialgebra. We define U-H(R) using the fact that A(H)(R) has a natural braiding in the category. In particular this shows that Manin's and FRT constructions work for superalgebras and G graded algebras.