2023/03/12 by Jens Hemelaer, Hemelaer, Jens
Mathematics · #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2303.06781
openalex publication_date 2023/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let M be a monoid that is embeddable in a group. We consider the topos PSh(M) of sets equipped with a right M-action, and we study the subtoposes that are of monoid type, i.e. the subtoposes that are again of the form PSh(N) for N a monoid. Our main result is that every subtopos of monoid type can be obtained by localization at a prime ideal of M. Conversely, we show that localization at a prime ideal produces a subtopos if and only if M has the right Ore property with respect to the complement of the prime ideal. We demonstrate our calculations in some examples: free monoids, two monoids related to the Connes-Consani Arithmetic Site, and torus knot monoids.