The Derived Auslander--Iyama Corresponence, a recent result of the authors, provides a classification up to quasi-isomorphism of the derived endomorphism algebras of basic dZ-cluster tilting objects in Hom-finite algebraic triangulated categories in terms of a small amount of algebraic data. In this note we highlight the role of minimal A_-algebra structures in the proof of this result, as well as the crucial role of the enhanced A_-obstruction theory developed by the second-named author.
Jasso et al. (Tue,) studied this question.