On k-invariants for $(\infty, n)$-categories
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866918025903472640 |
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| author | Harpaz, Yonatan Nuiten, Joost Prasma, Matan |
| author_facet | Harpaz, Yonatan Nuiten, Joost Prasma, Matan |
| contents | Every $(\infty, n)$-category can be approximated by its tower of homotopy $(m, n)$-categories. In this paper, we prove that the successive stages of this tower are classified by k-invariants, analogously to the classical Postnikov tower for spaces. Our proof relies on an abstract analysis of Postnikov-type towers equipped with k-invariants, and also yields a construction of k-invariants for algebras over $\infty$-operads and enriched $\infty$-categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2011_12723 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On k-invariants for $(\infty, n)$-categories Harpaz, Yonatan Nuiten, Joost Prasma, Matan Algebraic Topology Category Theory Every $(\infty, n)$-category can be approximated by its tower of homotopy $(m, n)$-categories. In this paper, we prove that the successive stages of this tower are classified by k-invariants, analogously to the classical Postnikov tower for spaces. Our proof relies on an abstract analysis of Postnikov-type towers equipped with k-invariants, and also yields a construction of k-invariants for algebras over $\infty$-operads and enriched $\infty$-categories. |
| title | On k-invariants for $(\infty, n)$-categories |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2011.12723 |