A non-commutative Priestley duality. (Q390415)

Skew lattices are a non-commutative generalization of lattices. The present paper establishes a duality (dual equivalence) between the category of left-handed strongly distributive skew lattices with zero and a category of sheaves over local Priestley spaces. This generalizes both the well-known Priestley duality for (bounded) distributive lattices and a recently developed Stone duality for skew Boolean algebras. The construction also provides a canonical embedding of these skew lattices into skew lattices of partial functions with the operations given by restriction and override.