双功能和身高
Ambidexterity and Height
摘要：
引入并研究了高阶半加性$\infty$ -范畴的\emph{semiadditive height}概念，它推广了色高.我们表明，更高的半加性结构trivializes以上的高度，并证明了一种形式的红移原则，其中分类增加了一个高度。在稳定的设置，我们表明，一个更高的半加性$\infty$范畴分解成产品根据高度，并与高度的概念，局部系统的半简单性。我们把更高的半加性和稳定性的研究在一般的框架下粉碎本地化的$Pr^{L}$，我们称之为\emph{modes}。利用这一理论，我们引入并研究了半可加高度$n$的泛稳定$\infty$ -半可加$\infty$ -范畴，给出了稳定$1$ -半可加$\infty$ -范畴是$\infty$ -半可加的充分条件.
英文摘要：
We introduce and study the notion of \emph{semiadditive height} for higher semiadditive $\infty$-categories, which generalizes the chromatic height. We show that the higher semiadditive structure trivializes above the height and prove a form of the redshift principle, in which categorification increases the height by one. In the stable setting, we show that a higher semiadditive $\infty$-category decomposes into a product according to height, and relate the notion of height to semisimplicity properties of local systems. We place the study of higher semiadditivity and stability in the general framework of smashing localizations of $Pr^{L}$, which we call \emph{modes}. Using this theory, we introduce and study the universal stable $\infty$-semiadditive $\infty$-category of semiadditive height $n$, and give sufficient conditions for a stable $1$-semiadditive $\infty$-category to be $\infty$-semiadditive.
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