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arXiv · 1709.09935

2-Segal spaces as invertible infinity-operads

Tashi Walde
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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 $\Lambda$.

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Tashi Walde. 2017-09-28. 2-Segal spaces as invertible infinity-operads. https://doi.org/10.2140/agt.2021.21.211

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