The Duality Between Algebraic Posets and Bialgebraic Frames: A Lattice Theoretic Perspective

this paper sets two goals. the first is to present algebraists with a purely order-theoretic derivation of the adjunction between the category dcpo of dcpos (directed complete posets) and the category frm of frames. this adjunction restricts to several stone-type dualities which are well-known and of considerable interest to computer scientists. the second goal is to describe the object classes of these subdualities in terms familiar to algebraists, thereby making a large body of literature about them more accessible.