论文标题
Quasi-2-Segal集
Quasi-2-Segal sets
论文作者
论文摘要
我们表明，Dyckerhoff-Kapranov和Gálvez-Kock-tonks的2个七分段空间（也称为分解空间）在简单集中具有自然的模拟，我们称之为Quasi-2-Segal套件，这两个想法享有与Quasi类别相似的相似关系，就像是一个segal Space相似的关系。特别是，我们在简单集的类别上构建了模型结构，其原始物体是准2个隔离集，该集合与完整的2个隔离空间的模型结构相当于quillen（我们的完整性概念来自Segal Space的完整性表征之一）。我们还证明了一个路径空间标准，该标准说，当且仅当其路径空间（也称为décalage）是准类别以及边缘细分标准时，简单集是一个准2个segal集。
We show that the 2-Segal spaces (also called decomposition spaces) of Dyckerhoff-Kapranov and Gálvez-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 décalage) are quasi-categories, as well as an edgewise subdivision criterion.
