An ordered sheaf representation of subresiduated lattices

Kennison's concept of an ordered sheaf is used to show that any member of the variety of subresiduated lattices is canonically isomorphic to the algebra of all ordered sections in a certain ordered sheaf, whose base is the Priestley space of the residuating sublattice.

Coproducts of De Morgan algebras

The dual of the category of De Morgan algebras is described in terms of compact totally ordered-disconnected ordered topological spaces which possess an involutorial homeomorphism that is also a dual order-isomorphism. This description is used to study the coproduct of an arbitrary collection of De Morgan algebras and also to represent the coproduct of two De Morgan algebras in terms of the continuous order-preserving functions from the Priestley space of one algebra to the other algebra, endowed with the discrete topology. In addition, it is proved that the coproduct of a family of Kleene algebras in the category of De Morgan algebras is the same as the coproduct in the subcategory of Kleene algebras if and only if at most one of the algebras is not boolean.