Monadic representation of Scott information systems
by
Ales Pultr
Charles University
Coauthors: Bernhard Banaschewski (McMaster University)

Consider the category SLat of bounded meet-semilattices and ( /\ , 0, 1)-homomorphisms. The down-set functor D:SLat --> SLat together with the natural transformations \mu = (U --> \cup U):D o D --> D and \eta = (a --> \downarrow a):Id --> D obviously constitutes a monad D.

It is easy to see (and certainly well-known) that the category SLat^D of monadic algebras is the category of frames. The question naturally arises as to whether the corresponding Kleisli category SLat_D is not also (equivalent to) some well known category. It is: it turns out that it is (the dual of) the category of Scott domains (or, equivalently, the category of Scott information systems with approximable maps).

Date received: June 6, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeq-39.