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The $\infty$–categorical Eckmann–Hilton argument

Tomer M Schlank and Lior Yanovski

Algebraic & Geometric Topology 19 (2019) 3119–3170
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 PQ is (d1+d2+2)–connected. We consider this to be a natural –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