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Bibliographic Details
Main Author: Liu, Yu Leon
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2408.05607
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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