Date: Thu, 13 Oct 1994 10:23:33 +0100 From: Frank Piessens <Frank.Piessens@cs.kuleuven.ac.be>
Can somebody give me references to literature on Burroni's graphical algebras? The only paper I know of is:
"Algebres graphiques" (A. Burroni), Cahiers de Topologie et Geometrie Differentielle, XXII, 1981.
Many thanks,
Frank Piessens. Frank.Piessens@cs.kuleuven.ac.be
This is certainly the primary reference. Unfortunately there were problems with Burroni's original proof that {toposes + logical morphisms} is monadic over GRAPH. These are dealt with in E.J. Dubuc and G.M. Kelly. "A presentation of topoi as algebraic relative to categories or graphs", Journal of Algebra (81), 1983, 420-433. There is also a certain amount of material on the example of toposes in J. Lambek and P.J. Scott. "Introduction to Higher Order Categorical Logic", CUP, 1986. I suppose the main point of graphical algebras is that they give a syntax for describing any category finitarily monadic over GRAPH as a category of "algebras". A proof of that was known to Kelly at a quite early stage, but can be recovered from the general machinery in G.M. Kelly and A.J. Power. "Adjunctions whose units are coequalizers, and presentations of finitary enriched monads", Jounal of Pure and Applied Algebra 89 (1993), 163-179 There is also an account in my survey: "Variations on Algebra: monadicity and generalisations of algebraic theories", Sussex University Computer Science Technical Report 6/94, 1994. all best wishes, Edmund