Monoid Properties as Invariants of Toposes of Monoid Actions

@article{Hemelaer2020MonoidPA,
  title={Monoid Properties as Invariants of Toposes of Monoid Actions},
  author={Jens Hemelaer and Morgan Rogers},
  journal={arXiv: Category Theory},
  year={2020}
}
We systematically investigate, for a monoid $M$, how topos-theoretic properties of $\mathbf{PSh}(M)$, including the properties of being atomic, strongly compact, local, totally connected or cohesive, correspond to semigroup-theoretic properties of $M$. 
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