  We show that the representation category of the quantum group of a
non-degenerate bilinear form is monoidally equivalent to the representation
category of the quantum group SL_q(2), for a well chosen non-zero parameter q.
The main ingredient for the proof of this result is the direct and explicit
construction of an appropriate Hopf bigalois extension. Then we get, in
characteristic zero, a full description of cosemisimple Hopf algebras whose
representation semi-ring is isomorphic to the one of SL(2).
