Toposes of Monoid Actions
Abstract
We study toposes of actions of monoids on sets. We begin with ordinary actions, producing a class of presheaf toposes which we characterize. As groundwork for considering topological monoids, we branch out into a study of supercompactly generated toposes (a class strictly larger than presheaf toposes). This enables us to efficiently study and characterize toposes of continuous actions of topological monoids on sets, where the latter are viewed as discrete spaces. Finally, we refine this characterization into necessary and sufficient conditions for a supercompactly generated topos to be equivalent to a topos of this form.
Keywords
Cite
@article{arxiv.2112.10198,
title = {Toposes of Monoid Actions},
author = {Morgan Rogers},
journal= {arXiv preprint arXiv:2112.10198},
year = {2021}
}
Comments
PhD thesis presented for the degree of Doctor of Philosophy in Computer Science and Mathematics of Computation; supervised by Olivia Caramello. Supported by INdAM and the Marie Sklodowska-Curie Actions as a part of the INdAM Doctoral Programme in Mathematics and/or Applications Cofunded by Marie Sklodowska-Curie Actions (INdAM-DP-COFUND-2015, grant number 713485). 238 pages