On Colimits and Model Structures in Various Categories of Manifolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866910576099196928 |
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| author | White, David |
| author_facet | White, David |
| contents | After explaining the importance of model categories in abstract homotopy theory, we provide concrete examples demonstrating that various categories of manifolds do not have all finite colimits, and hence cannot be model categories. We then consider various enlargements of our categories of manifolds, culminating in categories of presheaves. We explain how to produce model structures on these enlarged categories, culminating with answering an open problem involving Poincaré spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_15511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Colimits and Model Structures in Various Categories of Manifolds White, David Algebraic Topology After explaining the importance of model categories in abstract homotopy theory, we provide concrete examples demonstrating that various categories of manifolds do not have all finite colimits, and hence cannot be model categories. We then consider various enlargements of our categories of manifolds, culminating in categories of presheaves. We explain how to produce model structures on these enlarged categories, culminating with answering an open problem involving Poincaré spaces. |
| title | On Colimits and Model Structures in Various Categories of Manifolds |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2405.15511 |