  We consider the category of C*-algebras equipped with actions of a locally
compact quantum group. We show that this category admits a monoidal structure
satisfying certain natural conditions if and only if the group is
quasitriangular. The monoidal structures are in bijective correspondence with
unitary R-matrices. To prove this result we use only very natural properties
imposed on considered monoidal structures. We assume that monoidal product is a
crossed product, monoidal product of injective morphisms is injective and that
monoidal product reduces to the minimal tensor product when one of the involved
C*-algebras is equipped with a trivial action of the group. No a priori form of
monoidal product is used.
