Derived equivalences induced by nonclassical tilting objects

Suppose that A is an abelian category whose derived category whose derived category D(A) has Hom sets and arbitrary (small) coproducts, let T be a (not necessarily classical) (n-)tilting object of A and let H be the heart of the associated t-structure on D(A). We show that there is a triangulated equivalence of unbounded derived categories between D(H) and D(A) which is compatible with the inclusion functor of H into D(A). The result admits a straightforward dualization to cotilting objects in abelian categories whose derived category has Hom sets and arbitrary products.