$\mathbb{E}_n$-algebras in m-categories
Yu Leon Liu

TL;DR
This paper establishes a connectivity bound for maps of $ $-operads and introduces an inductive method to construct $ $-algebras within $m$-categories, advancing the understanding of higher algebraic structures.
Contribution
It provides a new connectivity bound for $ $-operad maps and an inductive construction technique for $ $-algebras in $m$-categories, utilizing a novel Eckmann-Hilton argument.
Findings
Proved a connectivity bound for maps of $ $-operads.
Developed an inductive construction method for $ $-algebras in $m$-categories.
Established a Blakers-Massey type statement for algebras of coherent $ $-operads.
Abstract
We prove a connectivity bound for maps of -operads of the form , and as a consequence, give an inductive way to construct -algebras in -categories. The result follows from a version of Eckmann-Hilton argument that takes into account both connectivity and arity of -operads. Along the way, we prove a technical Blakers-Massey type statement for algebras of coherent -operads.
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Taxonomy
TopicsAdvanced Algebra and Logic · Rings, Modules, and Algebras · Fuzzy and Soft Set Theory
