  We show how Stone duality can be extended from maps to relations. This is
achieved by working order enriched and defining a relation from A to B as both
an order-preserving function from the opposite of A times B to the 2-element
chain and as a subobject of A times B. We show that dual adjunctions and
equivalences between regular categories, taken in a suitably order enriched
sense, extend to (framed bi)categories of relations.
