  We define the notion of a Kirby element of a ribbon category C (not
necessarily semisimple). Kirby elements lead to 3-manifolds invariants. We
characterize (in terms of the structure maps of some categorical Hopf algebra)
a set of Kirby elements of C which is sufficiently large to recover the known
quantum invariants computed from C. The cases of a semisimple ribbon category
and of a category of representations are explored in details.
