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$2$-Segal spaces as invertible $\infty$-operads. (arXiv:1709.09935v1 [math.AT])

来源于:arXiv
We exhibit the simplex category $\Delta$ as an $\infty$-categorical localization of the category $\Omega_\pi$ of plane rooted trees introduced by Moerdijk and Weiss. As an application we obtain an equivalence of $\infty$-categories between $2$-Segal simplicial spaces as introduced by Dyckerhoff and Kapranov and invertible non-symmetric $\infty$-operads. In addition, we prove analogous results where $\Delta$ is replaced by Connes' cyclic category $\Lambda$, the category of finite pointed sets or the category of non-empty finite sets; the corresponding categories of trees are given by plane trees, rooted trees and abstract trees, respectively. 查看全文>>