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Idempotents and the points of the topos of M-sets

2020/11/23 by Ilia Pirashvili, Pirashvili, Ilia
Mathematics · Computer Science · #Homotopy and Cohomology in Algebraic Topology #semigroups and automata theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2011.11747

Abstract

The aim of this paper is to study the points and localising subcategories of the topos of M-sets, for a finite monoid M. We show that the points of this topos can be fully classified using the idempotents of M. We introduce a topology on the iso-classes of these points, which differs from the classical topology introduced in SGA4. Likewise, the localised subcategories of the topos M-sets correspond to the set of all two-sided idempotent Ideals of M.

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