Homomorphisms of complete distributive lattices

Abstract

The category of all complete distributive lattices and their complete homomorphisms is universal, and this is also true for the category of all complete distributive lattices whose morphisms preserve complete joins, finite meets and an additional nullary operation. A survey of analogous results on algebraic universality of categories based on finitary distributive (0, 1)-lattices is included to motivate further questions about categories based on complete distributive lattices.

Keywords: complete distributive lattice, complete lattice homomorphism, frame, Heyting algebra, continuous map, universal category

Quaestiones Mathematicae 23(2000), 259–268