• Corpus ID: 245334807

Toposes of Monoid Actions

@inproceedings{Rogers2021ToposesOM,
  title={Toposes of Monoid Actions},
  author={Morgan Rogers},
  year={2021}
}
In our thesis, which is based on [1], [2], [3] and [4], we studied toposes of actions of monoids on sets. We began with ordinary actions, producing a class of presheaf toposes which we characterized. As groundwork for considering topological monoids, we branched out into a study of supercompactly generated toposes (a class strictly larger than presheaf toposes). This enabled us to efficiently study and characterize toposes of continuous actions of topological monoids on sets, where the latter… 
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Toposes of Topological Monoid Actions
We demonstrate that categories of continuous actions of topological monoids on discrete spaces are Grothendieck toposes. We exhibit properties of these toposes, giving a solution to the corresponding

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We present and characterize the classes of Grothendieck toposes having enough supercompact objects or enough compact objects. In the process, we examine the subcategories of supercompact objects and
Monoid Properties as Invariants of Toposes of Monoid Actions
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,
Toposes of Discrete Monoid Actions
Properties of toposes of right $M$-sets are studied, and these toposes are characterised up to equivalence by their canonical points. The solution to the corresponding Morita equivalence problem is
2021 (Former) Marie Sklodowska-Curie fellow of the Istituto Nazionale di Alta Matematica at Università degli Studi dell
  • Toposes of Topological Monoid Actions, Compositionality (submitted)