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.

Toposes of monoid actions / Morgan Rogers , 2021 Dec 14. 34. ciclo, Anno Accademico 2020/2021.

Toposes of monoid actions

ROGERS, MORGAN
2021-12-14

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.
14-dic-2021
topos theory; monoid action
Toposes of monoid actions / Morgan Rogers , 2021 Dec 14. 34. ciclo, Anno Accademico 2020/2021.
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Descrizione: Toposes of Monoid Actions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2126152
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