  Distributive Stonean residuated lattices are closely related to Stone
algebras since their bounded lattice reduct is a Stone algebra. In the present
work we follow the ideas presented by Chen and Gr\"{a}tzer and try to apply
them for the case of Stonean residuated lattices. Given a Stonean residuated
lattice, we consider the triple formed by its Boolean skeleton, its algebra of
dense elements and a connecting map. We define a category whose objects are
these triples and suitably defined morphisms, and prove that we have a
categorical equivalence between this category and that of Stonean residuated
lattices. We compare our results with other works and show some applications of
the equivalence.
