Categorical resolution of singularities

Building on the concept of a smooth DG algebra we define the notion of a smooth derived category. We then propose the definition of a categorical resolution of singularities. Our main example is the derived category D(X) of quasi-coherent sheaves on a scheme X. We prove that D(X) has a canonical categorical resolution if the base field is perfect and X is a separated scheme of finite type with a dualizing complex.