论文标题
$ \ mathbf {z} $ - 类别i
$\mathbf{Z}$-Categories I
论文作者
论文摘要
本文是两篇论文中的第一本，$ \ mathbf {z} $ - 类别i和$ \ mathbf {z} $ - 类别II，它发展了$ \ m m i \ mathbf {z} $ - 类别的概念$ \ left（\ infty，1 \ right）$ - 同型相干$ \ mathbf {z} $ - 类别为尖的群体。 在这项工作中，我们提供了\ cite {kan}组合光谱的$ 2 $类别处理，并认为此描述是同型相干$ \ mathbf {z} $类别的持久概念的简单化头像。然后，我们在$ 2 $ - 类别的$ 2 $类别中开发了限制理论，其中包括Berger，Mellies和Weber，以提供蜂窝类别，该类别是$ \ Mathbf {z} $ - 类别为$ \ triangle $ to $ 1 $ - 类别或$θ_{n} $是$ n $ n $ n $ n $ - categories。在附录中，我们提供了20 $^{\ mathrm {th}} $ century稳定同型理论的光谱函数的概括。
This paper is the first in a series of two papers, $\mathbf{Z}$-Categories I and $\mathbf{Z}$-Categories II, which develop the notion of $\mathbf{Z}$-category, the natural bi-infinite analog to strict $ω$-categories, and show that the $\left(\infty,1\right)$-category of spectra relates to the $\left(\infty,1\right)$-category of homotopy coherent $\mathbf{Z}$-categories as the pointed groupoids. In this work we provide a $2$-categorical treatment of the combinatorial spectra of \cite{Kan} and argue that this description is a simplicial avatar of the abiding notion of homotopy coherent $\mathbf{Z}$-category. We then develop the theory of limits in the $2$-category of categories with arities of Berger, Mellies, and Weber to provide a cellular category which is to $\mathbf{Z}$-categories as $\triangle$ is to $1$-categories or $Θ_{n}$ is to $n$-categories. In an appendix we provide a generalization of the spectrification functors of 20$^{\mathrm{th}}$ century stable homotopy theory in the language of category-weighted limits.
