Monadic functors forgetful of (dis)inhibited actions
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911252169621504 |
|---|---|
| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | We prove a number of results of the following common flavor: for a category $\mathcal{C}$ of topological or uniform spaces with all manner of other properties of common interest (separation / completeness / compactness axioms), a group (or monoid) $\mathbb{G}$ equipped with various types of topological structure (topologies, uniformities) and the corresponding category $\mathcal{C}^{\mathbb{G}}$ of appropriately compatible $\mathbb{G}$-flows in $\mathcal{C}$, the forgetful functor $\mathcal{C}^{\mathbb{G}}\to \mathcal{C}$ is monadic. In all cases of interest the domain category $\mathcal{C}^{\mathbb{G}}$ is also cocomplete, so that results on adjunction lifts along monadic functors apply to provide equivariant completion and/or compactification functors. This recovers, unifies and generalizes a number of such results in the literature due to de Vries, Mart'yanov and others on existence of equivariant compactifications / completions and cocompleteness of flow categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_13169 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monadic functors forgetful of (dis)inhibited actions Chirvasitu, Alexandru Category Theory General Topology 18C15, 18D20, 18A30, 18A40, 54D35, 54E15, 54A20, 22F05 We prove a number of results of the following common flavor: for a category $\mathcal{C}$ of topological or uniform spaces with all manner of other properties of common interest (separation / completeness / compactness axioms), a group (or monoid) $\mathbb{G}$ equipped with various types of topological structure (topologies, uniformities) and the corresponding category $\mathcal{C}^{\mathbb{G}}$ of appropriately compatible $\mathbb{G}$-flows in $\mathcal{C}$, the forgetful functor $\mathcal{C}^{\mathbb{G}}\to \mathcal{C}$ is monadic. In all cases of interest the domain category $\mathcal{C}^{\mathbb{G}}$ is also cocomplete, so that results on adjunction lifts along monadic functors apply to provide equivariant completion and/or compactification functors. This recovers, unifies and generalizes a number of such results in the literature due to de Vries, Mart'yanov and others on existence of equivariant compactifications / completions and cocompleteness of flow categories. |
| title | Monadic functors forgetful of (dis)inhibited actions |
| topic | Category Theory General Topology 18C15, 18D20, 18A30, 18A40, 54D35, 54E15, 54A20, 22F05 |
| url | https://arxiv.org/abs/2404.13169 |