A duality for the category of directed multigraphs

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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.

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Thursday, November 20, 1997
4:10 p.m. in MA 109
Coffee/Tea/Treats 3:30 p.m. in MA 104 (Lounge)

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