The ∞-categorical Eckmann-Hilton argument

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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 (Formula Presented.) is (d1+d2+2)-connected. We consider this to be a natural ∞-categorical generalization of the classical Eckmann-Hilton argument.

Original languageAmerican English
Pages (from-to)3119-3170
Number of pages52
JournalAlgebraic and Geometric Topology
Volume19
Issue number6
DOIs
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019, Mathematical Sciences Publishers. All rights reserved.

Keywords

  • Eckmann–Hilton argument
  • Infinity operads

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