论文标题
通过部分松弛的限制，全球同义理论
Global homotopy theory via partially lax limits
论文作者
论文摘要
我们为不稳定且稳定的全球同型理论提供新的$ \ infty $分类模型。我们使用部分松弛限制的概念正式化了一个全局对象是$ g $ - 对象的集合，每个紧凑型Lie Group $ g $都与限制通气函数兼容。更确切地说，我们表明，全球空间的$ \ infty $ - 类别相当于函数的部分宽松限制，该函数将紧凑的Lie Group $ g $发送给$ g $ spaces的$ \ infty $ -Stegory。我们还证明了此结果的稳定版本，这表明全球光谱的$ \ infty $ - 类别等于$ g $ spectra的部分图表。最后，以前情况下使用的技术使我们能够描述一个适合$ g $ -spectra的$ \ infty $ - $ g $ g $的$ g $ -spectra，限制了$ h $ spectra的限制，$ h $ spectra的$ h $在所有紧凑型子组上运行的$ h $。
We provide new $\infty$-categorical models for unstable and stable global homotopy theory. We use the notion of partially lax limits to formalize the idea that a global object is a collection of $G$-objects, one for each compact Lie group $G$, which are compatible with the restriction-inflation functors. More precisely, we show that the $\infty$-category of global spaces is equivalent to a partially lax limit of the functor sending a compact Lie group $G$ to the $\infty$-category of $G$-spaces. We also prove the stable version of this result, showing that the $\infty$-category of global spectra is equivalent to the partially lax limit of a diagram of $G$-spectra. Finally, the techniques employed in the previous cases allow us to describe the $\infty$-category of proper $G$-spectra for a Lie group $G$, as a limit of a diagram of $H$-spectra for $H$ running over all compact subgroups of $G$.
