From CM-finite to CM-free

We prove a generalization of the stability for Gorenstein categories in [36] and [24]; and show that the relative Auslander algebra of a CM-finite algebra is CM-free. On the other hand, we describe the bounded derived category, and the Gorenstein defect category introduced in [11], via Gorenstein-projective objects; and we show that the Gorenstein defect category of a CM-finite algebra is triangle-equivalent to the singularity category of its relative Auslander algebra.