论文标题
关于两个球形曲折的组成
On the composition of two spherical twists
论文作者
论文摘要
E. segal证明，增强三角类别的任何自动等效性都可以将其视为球形扭曲。但是，当以球形扭转为单位时，表现出自动等效性时，对于球形函数的源类别有各种选择。我们描述了一种结构，该结构将两个球形曲折的组成是一个围绕单个球形函数的扭曲，其源类别的半双轴分解为我们开始使用的球形函数的源类别。我们给出了该球形函子的CotWist的描述，并在特殊情况下证明，当我们的起始曲折围绕球形对象时，cotwist是serre functor（直至移动）。我们对P-Objects的明确处理结束。
E. Segal proved that any autoequivalence of an enhanced triangulated category can be realised as a spherical twist. However, when exhibiting an autoequivalence as a spherical twist one has various choices for the source category of the spherical functor. We describe a construction that realises the composition of two spherical twists as the twist around a single spherical functor whose source category semiorthogonally decomposes into the source categories for the spherical functors we started with. We give a description of the cotwist for this spherical functor and prove, in the special case when our starting twists are around spherical objects, that the cotwist is the Serre functor (up to a shift). We finish with an explicit treatment for the case of P-objects.
