  We show that complex semisimple quantum groups, that is, Drinfeld doubles of
$ q $-deformations of compact semisimple Lie groups, satisfy a categorical
version of the Baum-Connes conjecture with trivial coefficients. This approach,
based on homological algebra in triangulated categories, is compatible with the
previously studied deformation picture of the assembly map, and allows us to
define an assembly map with arbitrary coefficients for these quantum groups.
