Contravariant Koszul duality between non-positive and positive dg algebras

Abstract

We characterize locally finite non-positive dg algebras that arise as Koszul duals of locally finite non-positive dg algebras. Moreover, we show that the Koszul dual functor induces contravariant derived equivalnces. As a consequence, we prove that every functorially finite bounded heart of $\pvd A$ of a locally finite non-positive dg algebra is a length category.