2–Segal spaces as invertible infinity-operads
2–Segal spaces as invertible infinity-operads
复制标题
2-Segal 空间作为可逆无穷运算
DOI：
10.2140/agt.2021.21.211
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Tashi Walde
中科院分区：
文献类型：
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作者：
Tashi Walde
我们展示了单纯形范畴$\Delta$作为Moerdijk和韦斯引入的平面根树范畴$\Omega_\pi$的一个$\infty$-范畴局部化。作为应用，我们得到了Dyckerhoff和Kapranov引入的$2$-Segal单纯空间与可逆非对称$\infty$-运算之间的$\infty$-范畴的等价性.另外，我们证明了类似的结果，其中$\Delta$被Connes的循环范畴$\Lambda$、有限点集范畴或非空有限集范畴所取代，相应的树范畴分别由平面树、根树和抽象树给出.
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.
DOI：
10.4171/jems/791
发表时间：
2018
期刊：
arXiv: Algebraic Geometry
影响因子：
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作者：
T. Dyckerhoff;M. Kapranov
通讯作者：
M. Kapranov