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math.CT2021
Toposes of Monoid Actions
Morgan Rogers
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 topologic…
math.CT2021★ 6 cited
Toposes of Topological Monoid Actions
Morgan Rogers
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 t…
math.CT2021
On Supercompactly and Compactly Generated Toposes
Morgan Rogers
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 superc…