  Suppose that $\mathcal{A}$ is an abelian category whose derived category
$\mathcal{D}(\mathcal{A})$ has $Hom$ sets and arbitrary (small) coproducts, let
$T$ be a (not necessarily classical) ($n$-)tilting object of $\mathcal{A}$ and
let $\mathcal{H}$ be the heart of the associated t-structure on
$\mathcal{D}(\mathcal{A})$. We show that the inclusion functor
$\mathcal{H}\hookrightarrow\mathcal{D}(\mathcal{A})$ extends to a triangulated
equivalence of unbounded derived categories
$\mathcal{D}(\mathcal{H})\stackrel{\cong}{\longrightarrow}\mathcal{D}(\mathcal{A})$.
The result admits a straightforward dualization to cotilting objects in abelian
categories whose derived category has $Hom$ sets and arbitrary products.
