More on graphic toposes. (English) Zbl 0759.18004

Lawvere, F. William

Cah. Topologie Géom. Différ. Catég. 32, No. 1, 5-10 (1991).

A monoid is called graphic if the identity \(aba=ab\) holds. This paper studies the category (topos) of sets with a right action by such monoid. The ordered set of essential subtoposes is easy to calculate, and thus serves as a testing ground for reflections on intrinsic dimension notions deriving from the author’s rendering of Hegel’s “Aufhebung” relation. A more comprehensive treatment of the latter appears in the author’s “Display of graphics and their application, as exemplified by 2- categories and the Hegelian taco” [in: Proc. First Int. Conf. Algebraic Methodology and Software Technology, Univ. Iowa, 51-75 (1989)].

Reviewer: A.Kock (Aarhus)

MSC:

18B25	Topoi
20M35	Semigroups in automata theory, linguistics, etc.
18B20	Categories of machines, automata

Keywords:

graphic toposes; graphic monoid; monoid action; Hegel’s Aufhebung relation; ordered set of essential subtoposes; dimension

References:

[1]	F.W. Lawvere , Qualitative distinctions between some toposes of generalized graphs , Proceedings of AMS Boulder 1987 Symposium on Category Theory and Computer Science, Contemporary Mathematics 92 ( 1989 ) 261 - 299 . MR 1003203 | Zbl 0675.18003 · Zbl 0675.18003
[2]	G.M. Kelly & F.W. Lawvere , On the, Complete Lattice of Essential Localizations , Bull. Société Mathematique de Belgique , XLI ( 1989 ) 289 - 319 . MR 1031753 | Zbl 0686.18005 · Zbl 0686.18005
[3]	F.W. Lawvere , Display of Graphics and their Applications, as Exemplified by 2-Categories and the Hegelian ”Taco” , Proceedings of the First International Conference on Algebraic Methodology and Software Technology, The University of Iowa , ( 1989 ) 51 - 75 .