Quasi-2-Segal sets

IF 0.8 Q2 MATHEMATICS Tunisian Journal of Mathematics Pub Date : 2022-04-05 DOI:10.2140/tunis.2023.5.327
M. Feller
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引用次数: 3

Abstract

We show that the 2-Segal spaces (also called decomposition spaces) of Dyckerhoff-Kapranov and G\'alvez-Kock-Tonks have a natural analogue within simplicial sets, which we call quasi-2-Segal sets, and that the two ideas enjoy a similar relationship as the one Segal spaces have with quasi-categories. In particular, we construct a model structure on the category of simplicial sets whose fibrant objects are the quasi-2-Segal sets which is Quillen equivalent to a model structure for complete 2-Segal spaces (where our notion of completeness comes from one of the equivalent characterizations of completeness for Segal spaces). We also prove a path space criterion, which says that a simplicial set is a quasi-2-Segal set if and only if its path spaces (also called d\'ecalage) are quasi-categories, as well as an edgewise subdivision criterion.
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Quasi-2-Segal集
我们证明了Dyckerhoff-Kapranov和G\'alvez-Kock-Tonks的2-Segal空间(也称为分解空间)在简单集(我们称之为拟2-Segal集)内具有自然的类似,并且这两个思想与Segal空间与拟范畴的关系相似。特别地,我们在以拟2-Segal集为对象的简单集的范畴上构造了一个模型结构,它与完全2-Segal空间的模型结构是Quillen等价的(其中我们的完备性概念来自于Segal空间完备性的等价表征之一)。我们还证明了一个路径空间准则,即当且仅当一个简单集的路径空间(也称为d\'ecalage)是拟范畴时,它是一个拟2- segal集,以及一个边缘细分准则。
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来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
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