## Algebraic & Geometric Topology

### The $\infty$–categorical Eckmann–Hilton argument

#### Abstract

We define a reduced $∞$–operad $P$ to be $d$–connected if the spaces $P(n)$ of $n$–ary operations are $d$–connected for all $n≥0$. Let $P$ and $Q$ be two reduced $∞$–operads. We prove that if $P$ is $d1$–connected and $Q$ is $d2$–connected, then their Boardman–Vogt tensor product $P⊗Q$ is $(d1+d2+2)$–connected. We consider this to be a natural $∞$–categorical generalization of the classical Eckmann–Hilton argument.

#### Article information

Source
Algebr. Geom. Topol., Volume 19, Number 6 (2019), 3119-3170.

Dates
Revised: 16 February 2019
Accepted: 26 February 2019
First available in Project Euclid: 29 October 2019

https://projecteuclid.org/euclid.agt/1572314551

Digital Object Identifier
doi:10.2140/agt.2019.19.3119

Mathematical Reviews number (MathSciNet)
MR4023337

Zentralblatt MATH identifier
07142627

#### Citation

Schlank, Tomer M; Yanovski, Lior. The $\infty$–categorical Eckmann–Hilton argument. Algebr. Geom. Topol. 19 (2019), no. 6, 3119--3170. doi:10.2140/agt.2019.19.3119. https://projecteuclid.org/euclid.agt/1572314551

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