Morgan Rogers - Toposes of Topological Monoid Actions

compositionality:13520 - Compositionality, January 10, 2023, Volume 5 (2023) -
Toposes of Topological Monoid ActionsArticle

Authors: Morgan Rogers ORCID1

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 Morita-equivalence problem. We characterize these toposes in terms of their canonical points. We identify natural classes of representatives with good topological properties, `powder monoids' and then `complete monoids', for the Morita-equivalence classes of topological monoids. Finally, we show that the construction of these toposes can be made (2-)functorial by considering geometric morphisms induced by continuous semigroup homomorphisms.

Volume: Volume 5 (2023)
Published on: January 10, 2023
Imported on: May 2, 2024
Keywords: Mathematics - Category Theory,Mathematics - Rings and Algebras,20M30, 22A25, 18F10

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