Algebraic Theories of Domains
by
Bob Flagg
University of Southern Maine

We study the problem of characterizing various categories of domains as algebras for monads over the categories of sets, posets or (subcategories of) topological spaces. A principal result is that the category of compact pospaces is algebraic over the category of posets. This asymmetric version of Manes' Theorem shows that the notion of compact pospace is algebraic in a precise sense and provides a useful tool for investigating these spaces. As a corollary we obtain the theorem of Simmons and Wyler which says that compact pospaces are also algebraic over the category of topological spaces and continuous maps. This makes explicit the connection between the Salbany and the prime Wallman compactifications.

Date received: June 30, 1997

Copyright © 1997 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 # caao-62.