  We give an alternative proof of the theorem by Kuznetsov and Lunts stating
that any separated scheme of finite type over a field of characteristic zero
admits a categorical resolution of singularities. Their construction makes use
of the fact that every variety (over a field of characteristic zero) can be
resolved by a finite sequence of blow-ups along smooth centres. We merely
require the existence of (projective) resolutions. To accomplish this we put
the $\mathcal{A}$-spaces of Kuznetsov and Lunts in a different light, viewing
them instead as schemes endowed with finite filtrations. The categorical
resolution is then constructed by gluing together differential graded
categories obtained from a hypercube of finite length filtered schemes.
