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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.05607 |
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| _version_ | 1866917746183241728 |
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| author | Liu, Yu Leon |
| author_facet | Liu, Yu Leon |
| contents | We prove a connectivity bound for maps of $\infty$-operads of the form $\mathbb{A}_{k_1} \otimes \cdots \otimes \mathbb{A}_{k_n} \to \mathbb{E}_n$, and as a consequence, give an inductive way to construct $\mathbb{E}_n$-algebras in $m$-categories. The result follows from a version of Eckmann-Hilton argument that takes into account both connectivity and arity of $\infty$-operads. Along the way, we prove a technical Blakers-Massey type statement for algebras of coherent $\infty$-operads. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05607 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\mathbb{E}_n$-algebras in m-categories Liu, Yu Leon Algebraic Topology Category Theory We prove a connectivity bound for maps of $\infty$-operads of the form $\mathbb{A}_{k_1} \otimes \cdots \otimes \mathbb{A}_{k_n} \to \mathbb{E}_n$, and as a consequence, give an inductive way to construct $\mathbb{E}_n$-algebras in $m$-categories. The result follows from a version of Eckmann-Hilton argument that takes into account both connectivity and arity of $\infty$-operads. Along the way, we prove a technical Blakers-Massey type statement for algebras of coherent $\infty$-operads. |
| title | $\mathbb{E}_n$-algebras in m-categories |
| topic | Algebraic Topology Category Theory |
| url | https://arxiv.org/abs/2408.05607 |