The ∞-categorical Eckmann-Hilton argument

Tomer M. Schlank; Lior Yanovski

doi:https://doi.org/10.2140/agt.2019.19.3119

The ∞-categorical Eckmann-Hilton argument

Tomer M. Schlank, Lior Yanovski

Einstein Institute of Mathematics

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	3119-3170
Number of pages	52
Journal	Algebraic and Geometric Topology
Volume	19
Issue number	6
DOIs	https://doi.org/10.2140/agt.2019.19.3119
State	Published - 2019

Keywords

Eckmann–Hilton argument
Infinity operads

All Science Journal Classification (ASJC) codes

Geometry and Topology

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https://doi.org/10.2140/agt.2019.19.3119

Cite this

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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.",

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AB - 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.

KW - Eckmann–Hilton argument

KW - Infinity operads

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M3 - مقالة

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VL - 19

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EP - 3170

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 6

ER -

The ∞-categorical Eckmann-Hilton argument

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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