Groupoidal completely distributive lattices

The Adamek and Pedicchio proof that top(op) is a quasi-variety is adapted t o show that the opposite of the category of pre-ordered sets is also a quas i-variety. The constructive proof given requires a description of power obj ects in terms of (constructively) completely distributive lattices and such a description is provided by the Carboni and Waiters notion of "groupoidal " object in a cartesian bicategory. (C) 1999 Elsevier Science B.V. All righ ts reserved. AMS Classification: 18B35; 06D10.