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2021 $2$–Segal spaces as invertible infinity-operads
Tashi Walde
Algebr. Geom. Topol. 21(1): 211-246 (2021). DOI: 10.2140/agt.2021.21.211

Abstract

We exhibit the simplex category Δ and Segal’s category Γ as –categorical localizations of the dendroidal categories Ωπ and Ω introduced by Moerdijk and Weiss. As an application we obtain an equivalence of –categories between invertible –operads and the 2–Segal spaces of Dyckerhoff and Kapranov. Finally, we describe a cyclic version of the dendroidal category and explain how it –localizes to Connes’ cyclic category Λ.

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Tashi Walde. "$2$–Segal spaces as invertible infinity-operads." Algebr. Geom. Topol. 21 (1) 211 - 246, 2021. https://doi.org/10.2140/agt.2021.21.211

Information

Received: 18 June 2019; Revised: 17 January 2020; Accepted: 29 January 2020; Published: 2021
First available in Project Euclid: 16 March 2021

Digital Object Identifier: 10.2140/agt.2021.21.211

Subjects:
Primary: 18D50 , 18G30

Keywords: $2$–Segal spaces , dendroidal objects , infinity-operads , simplicial objects

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 1 • 2021
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