#### Volume 21, issue 1 (2021)

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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 $\Delta$ and Segal’s category $\Gamma$ as $\infty$–categorical localizations of the dendroidal categories ${\Omega }_{\pi }$ and $\Omega$ 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 $\Lambda$.

##### Keywords
simplicial objects, $2$–Segal spaces, infinity-operads, dendroidal objects
##### Mathematical Subject Classification 2010
Primary: 18D50, 18G30