  Within the framework of braided or quasisymmetric monoidal categories braided
Q-supersymmetry is investigated, where Q is a certain functorial isomorphism in
a braided symmetric monoidal category. For an ordinary (co-)quasitriangular
Hopf algebra (H,R) a braided monoidal category of H-(co-)modules with braiding
induced by the R-matrix is considered. It can be shown for a specific class of
Q-supersymmetries in this category that every braided Q-super-Hopf algebra B
admits an ordinary Q-super-Hopf algebra structure on the cross product BxH such
that H is a sub-Hopf algebra and B is a subalgebra in BxH. Applying this
Q-bosonization to the quantum Koszul complex (K(q,g),d) of the quantum
enveloping algebra Uq(g) for Lie algebras g associated with the root systems A,
B, C and D one obtains a classical super-Hopf algebra structure on (K(q,g),d)
where the structure maps are morphisms of modules with differentiation.
