Duality for semilattice representations

AbstractThe paper presents general machinery for extending a duality between complete, cocomplete categories to a duality between corresponding categories of semilattice representations (i.e. sheaves over Alexandrov spaces). This enables known dualities to be regularized. Among the applications, regularized Lindenbaum-Tarski duality shows that the weak extension of Boolean logic (i.e. the semantics of PASCAL-like programming languages) is the logic for semilattice-indexed systems of sets. Another application enlarges Pontryagin duality by regularizing it to obtain duality for commutative inverse Clifford monoids