2–Segal spaces as invertible infinity-operads

Walde, Tashi

doi:10.2140/agt.2021.21.211

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$2$–Segal spaces as invertible infinity-operads

Tashi Walde

Algebraic & Geometric Topology 21 (2021) 211–246

DOI: 10.2140/agt.2021.21.211

Abstract

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

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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/

Volume 21, issue 1 (2021)