Algebraic & Geometric Topology

The $\infty$–categorical Eckmann–Hilton argument

Tomer M Schlank and Lior Yanovski

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We define a reduced –operad P to be d–connected if the spaces P(n) of n–ary operations are d–connected for all n0. 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.

Article information

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

Received: 3 September 2018
Revised: 16 February 2019
Accepted: 26 February 2019
First available in Project Euclid: 29 October 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18D05: Double categories, 2-categories, bicategories and generalizations 18D50: Operads [See also 55P48] 55P48: Loop space machines, operads [See also 18D50]

Eckmann–Hilton argument infinity operads


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.

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