The ∞–categorical Eckmann–Hilton argument

Schlank, Tomer; Yanovski, Lior

doi:10.2140/agt.2019.19.3119

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The $\infty$–categorical Eckmann–Hilton argument

Tomer M Schlank and Lior Yanovski

Algebraic & Geometric Topology 19 (2019) 3119–3170

DOI: 10.2140/agt.2019.19.3119

Abstract

We define a reduced $\infty$ –operad $P$ to be $d$ –connected if the spaces $P (n)$ of $n$ –ary operations are $d$ –connected for all $n \geq 0$ . Let $P$ and $Q$ be two reduced $\infty$ –operads. We prove that if $P$ is $d_{1}$ –connected and $Q$ is $d_{2}$ –connected, then their Boardman–Vogt tensor product $P \otimes Q$ is $(d_{1} + d_{2} + 2)$ –connected. We consider this to be a natural $\infty$ –categorical generalization of the classical Eckmann–Hilton argument.

Keywords

Eckmann–Hilton argument, infinity operads

Mathematical Subject Classification 2010

Primary: 18D05, 18D50, 55P48

References

Publication

Received: 3 September 2018

Revised: 16 February 2019

Accepted: 26 February 2019

Published: 20 October 2019

Authors

Tomer M Schlank
Einstein Institute of Mathematics Hebrew University of Jerusalem Jerusalem Israel

Lior Yanovski
Einstein Institute of Mathematics Hebrew University of Jerusalem Jerusalem Israel

Volume 19, issue 6 (2019)