Abstract Excision and $\ell^1$-Homology
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866929302499491840 |
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| author | Witzig, Johannes |
| author_facet | Witzig, Johannes |
| contents | We use the abstract setting of excisive functors in the language of $\infty$-categories to show that the best approximation to the $\ell^1$-homology functor by an excisive functor is trivial.
Then we make an effort to explain the used language on a conceptual level for those who do not feel at home with $\infty$-categories, prove that the singular chain complex functor is indeed excisive in the abstract sense, and show how the latter leads to classical excision statements in the form of Mayer-Vietoris sequences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_06120 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Abstract Excision and $\ell^1$-Homology Witzig, Johannes Algebraic Topology Category Theory 55N35, 55U35 (Primary), 18F50, 18N60 (Secondary) We use the abstract setting of excisive functors in the language of $\infty$-categories to show that the best approximation to the $\ell^1$-homology functor by an excisive functor is trivial. Then we make an effort to explain the used language on a conceptual level for those who do not feel at home with $\infty$-categories, prove that the singular chain complex functor is indeed excisive in the abstract sense, and show how the latter leads to classical excision statements in the form of Mayer-Vietoris sequences. |
| title | Abstract Excision and $\ell^1$-Homology |
| topic | Algebraic Topology Category Theory 55N35, 55U35 (Primary), 18F50, 18N60 (Secondary) |
| url | https://arxiv.org/abs/2203.06120 |