2-Segal spaces as invertible infinity-operads

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's cyclic category $\Lambda$.

25 pages. v5: restructured the paper to improve the presentation; added missing assumption to the key lemma; published

References in corpus (5)

• Decomposition spaces, incidence algebras and Möbius inversion I: basic theory
• Decomposition spaces, incidence algebras and Möbius inversion II: completeness, length filtration, and finiteness
• Decomposition spaces, incidence algebras and Möbius inversion III: the decomposition space of Möbius intervals
• Higher cyclic operads
• The dendroidal category is a test category

Cited by in corpus (3)

• Categories of graphs for operadic structures
• Quasi-2-Segal sets
• Segal conditions for generalized operads