On the differential graded Eilenberg-Moore construction

Abstract

The Eilenberg-Moore construction for modules over a differential graded monad is used to study a question of Balmer regarding existence of an exact adjoint pair representing an exact monad. A Bousfield-like localization for differential graded categories is realized as a special case of this construction using Drinfeld quotients. As applications, we study some example coming from G-equivariant triangulated categories and twisted derived categories.