A duality for the category of directed multigraphs
by
Dr. Richard Squire, Visiting Professor
Dept. of Mathematics
Eastern Washington University
The well known duality between the category of sets and the category of ccd (complete completely distributive) Boolean algebras given by the contravariant "subsets" functor, is extended to a duality between the category of graphs (directed multigraphs) and a category of ccd "graphic" algebras. Graphic algebras are Heyting algebras with one further unary operation, satisfying (in addition to the identities for Heyting algebras) one further identity. A Boolean algebra is a graphic algebra satisfying an obvious identity, and a set is construed as a graph having no arrows. The dualizing functor is the extension of the subsets functor to the contravariant subgraphs functor.
Thursday, November 20, 1997
4:10 p.m. in MA 109
Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)