  We present a categorical point of view on dynamical quantum groups in terms
of categories of Harish-Chandra bimodules. We prove Tannaka duality theorems
for forgetful functors into the monoidal category of Harish-Chandra bimodules
in terms of a slight modification of the notion of a bialgebroid. Moreover, we
show that the standard dynamical quantum groups $F(G)$ and $F_q(G)$ are related
to parabolic restriction functors for classical and quantum Harish-Chandra
bimodules. Finally, we exhibit a natural Weyl symmetry of the parabolic
restriction functor using Zhelobenko operators and show that it gives rise to
the action of the dynamical Weyl group.
