  We reanalyze the construction of the gravitational functional renormalization
group equation tailored to the Arnowitt-Deser-Misner formulation emphasizing
its connection to the covariant formulation. The results obtained from
projecting the renormalization group flow onto the Einstein-Hilbert action are
reviewed in detail and we provide a novel example illustrating how the
formalism may be connected to the Causal Dynamical Triangulations approach to
quantum gravity.
