  When a complex semisimple group $G$ acts holomorphically on a K\"ahler
manifold $(X,\omega)$ such that a maximal compact subgroup $K\subset G$
preserves the symplectic form $\omega$, a basic result of symplectic geometry
says that the corresponding categorical quotient $X/G$ can be identified with
quotient of the zero-set of the moment map by the action of $K$. We extend this
to the context of a semisimple group acting on a Sasakian manifold.
