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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2105.00772 |
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| _version_ | 1866909280016269312 |
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| author | Rogers, Morgan |
| author_facet | Rogers, Morgan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_00772 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Toposes of Topological Monoid Actions Rogers, Morgan Category Theory Rings and Algebras 20M30, 22A25, 18F10 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. |
| title | Toposes of Topological Monoid Actions |
| topic | Category Theory Rings and Algebras 20M30, 22A25, 18F10 |
| url | https://arxiv.org/abs/2105.00772 |