Categorical resolutions of a class of derived categories

By using the relative derived categories, we prove that if an Artin algebra \(A\) has a module \(T\) with \({\rm inj.dim}T<\infty\) such that \(^\perp T\) is finite, then the bounded derived category \(D^b(A\mbox{-}{\rm mod})\) admits a categorical resolution in the sense of [Kuz], and a categorical desingularization in the sense of [BO]. For CM-finite Gorenstein algebra, such a categorical resolution is weakly crepant. The similar results hold also for \(D^b(A\mbox{-}{\rm Mod})\).