On the structure of Calabi-Yau categories with a cluster tilting subcategory

Abstract

We prove that for d ≥ 2, an algebraic d-Calabi-Yau triangulated category endowed with a d-cluster tilting subcategory is the stable category of a DG category which is perfectly (d+1)-Calabi-Yau and carries a non degenerate t-structure whose heart has enough projectives.