The points and localisations of the topos of -sets

  • Ilia Pirashvili

    Universität Augsburg, Augsburg, Germany
The points and localisations of the topos of $M$-sets cover
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Abstract

In previous papers, we were able to prove that, much like in classical algebraic geometry, it is possible to recover our monoid scheme from the topos . This was achieved using topos points and localisations of . With this philosophy in mind, the aim of this paper is to study the topos of -sets for non-commutative monoids, especially their points and localisations. We will classify the points and localisations of -sets for finite monoids in terms of the idempotent elements of and idempotent ideals of , respectively. Some of the results obtained in this paper can already be found in previous works, in direct or indirect forms. See the last part of the introduction.

Cite this article

Ilia Pirashvili, The points and localisations of the topos of -sets. J. Noncommut. Geom. 18 (2024), no. 3, pp. 1103–1127

DOI 10.4171/JNCG/549