Groupoidal completely distributive lattices Original Research Article

The Adamek and Pedicchio proof that topop is a quasi-variety is adapted to show that the opposite of the category of pre-ordered sets is also a quasi-variety. The constructive proof given requires a description of power objects in terms of (constructively) completely distributive lattices and such a description is provided by the Carboni and Walters notion of “groupoidal” object in a cartesian bicategory.