Derived equivalences of functor categories (Q1621587)

In the present paper the authors study equivalences between derived categories associated to functor categories. In this way they obtain natural generalizations of some classical results already known for derived categories of module categories. In the mai result of the paper (Theorem 3.14) it is proved that if $\mathcal{S}$ is a small pre-additive category and $\mathcal{T}$ is a set of perfect complexes in from $\mathrm{Mod}\text{-}\mathcal{S}$ then the derived category associated to $\mathrm{Mod}\text{-}\mathcal{T}$ is equivalent to the relative derived category of $\mathrm{Mod}\text{-}\mathcal{S}$ with respect to $\mathcal{T}$. Moreover, this equivalence induces by restrictions between important subcategories of these derived categories. In the last part of the paper there are presented many applications. These include equivalences of homotopy categories or Gorenstein derived equivalences associated to right coherent rings.