Homotopical algebra is not concrete
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2017
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| _version_ | 1866912515228696576 |
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| author | Loregian, Fosco Di Liberti, Ivan |
| author_facet | Loregian, Fosco Di Liberti, Ivan |
| contents | We generalize Freyd's well-known result that "homotopy is not concrete", offering a general method to show that under certain assumptions on a model category $\mathcal M$, its homotopy category $\text{ho}(\mathcal M)$ cannot be concrete. This result is part of an attempt to understand more deeply the relation between set theory and abstract homotopy theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1704_00303 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Homotopical algebra is not concrete Loregian, Fosco Di Liberti, Ivan Category Theory Algebraic Topology Logic 18G55, 18E35, 18A22 We generalize Freyd's well-known result that "homotopy is not concrete", offering a general method to show that under certain assumptions on a model category $\mathcal M$, its homotopy category $\text{ho}(\mathcal M)$ cannot be concrete. This result is part of an attempt to understand more deeply the relation between set theory and abstract homotopy theory. |
| title | Homotopical algebra is not concrete |
| topic | Category Theory Algebraic Topology Logic 18G55, 18E35, 18A22 |
| url | https://arxiv.org/abs/1704.00303 |