论文标题
2类分类的操作纤维，Quillen的定理B和$ S^{ - 1} S $
2-categorical opfibrations, Quillen's Theorem B, and $S^{-1}S$
论文作者
论文摘要
在本文中，我们表明，沿任意2个函数的2类分类构型的严格和宽松的回调是同等的。我们提供两个申请。首先，我们证明了操作纤维模型的严格纤维均匀纤维。这是Quillen定理b的版本。其次，我们计算与操作纤维相关的同源频谱序列的$ E^2 $页面，并将此机械应用于$ S^{ - 1} S $的2类别结构。我们表明，如果$ s $是一种对称的单体2组，带有忠实的翻译，则$ s^{ - 1} s $模型$ s $的组完成。
In this paper we show that the strict and lax pullbacks of a 2-categorical opfibration along an arbitrary 2-functor are homotopy equivalent. We give two applications. First, we show that the strict fibers of an opfibration model the homotopy fibers. This is a version of Quillen's Theorem B amenable to applications. Second, we compute the $E^2$ page of a homology spectral sequence associated to an opfibration and apply this machinery to a 2-categorical construction of $S^{-1}S$. We show that if $S$ is a symmetric monoidal 2-groupoid with faithful translations then $S^{-1}S$ models the group completion of $S$.
