论文标题
稳定无穷大类别的球形元素辅助
Spherical monadic adjunctions of stable infinity categories
论文作者
论文摘要
本文涉及稳定的$ \ infty $ - 类别的球形附属及其与Monadic辅助的关系。我们从稳定$ \ infty $ - 类别的环境中的2/4属性开始证明球形附件的2/4属性。证明是基于对球形辅助的描述，即Halpern-Leistner，Shipman和Dyckerhoff，Kapranov，Schechtman，Soibelman给出的4个周期性半三相分解。然后，我们描述了由球体上局部系统引起的一类球形辅助示例。本文的主要结果是对单核辅助的球形性的表征。也就是说，只有且仅当扭曲函子是等效性并与单元的单位图上下班时，一个单核的邻接是球形的。这种特征是受埃德·西格尔（Ed Segal）作品的启发。
This paper concerns spherical adjunctions of stable $\infty$-categories and their relation to monadic adjunctions. We begin with a proof of the 2/4 property of spherical adjunctions in the setting of stable $\infty$-categories. The proof is based on the description of spherical adjunctions as 4-periodic semiorthogonal decompositions given by Halpern-Leistner, Shipman and by Dyckerhoff, Kapranov, Schechtman, Soibelman. We then describe a class of examples of spherical adjunctions arising from local systems on spheres. The main result of this paper is a characterization of the sphericalness of a monadic adjunctions in terms of properties of the monad. Namely, a monadic adjunction is spherical if and only if the twist functor is an equivalence and commutes with the unit map of the monad. This characterization is inspired by work of Ed Segal.
