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$2$–Segal spaces as invertible infinity-operads

Tashi Walde

Algebraic & Geometric Topology 21 (2021) 211–246
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.

Keywords
simplicial objects, $2$–Segal spaces, infinity-operads, dendroidal objects
Mathematical Subject Classification 2010
Primary: 18D50, 18G30
References
Publication
Received: 18 June 2019
Revised: 17 January 2020
Accepted: 29 January 2020
Published: 25 February 2021
Authors
Tashi Walde
Zentrum Mathematik
Technische Universität München
Garching bei München
Germany
https://www.math.uni-bonn.de/people/twalde/