Idempotents and the points of the topos of M-sets
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 $M$.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2020
- DOI:
- 10.48550/arXiv.2011.11747
- arXiv:
- arXiv:2011.11747
- Bibcode:
- 2020arXiv201111747P
- Keywords:
-
- Mathematics - Category Theory;
- 18B25;
- 20M14;
- 20M30