Toposes of Topological Monoid Actions
| Autor: | Morgan Rogers |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Compositionality. 5:1 |
| ISSN: | 2631-4444 |
| DOI: | 10.32408/compositionality-5-1 |
| Popis: | 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. 58 pages. Final version appearing in Compositionality. Project under the INdAM Doctoral Programme in Mathematics and/or Applications Cofunded by Marie Sklodowska-Curie Actions, INdAM-DP-COFUND-2015, grant number 713485 |
| Databáze: | OpenAIRE |
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