论文标题
Verdier二元性能的POSET
Posets for which Verdier duality holds
论文作者
论文摘要
我们讨论了两个已知的Sheaf-Cosheaf二元定理：有限常规CW复合体的面部和Lurie's的面部曲线，用于紧凑的Hausdorff空间，即协变量Verdier Duality。我们为他们提供统一的配方，并证明它们的概括。我们在球形频谱和更一般有限的POSET上的前者作品版本，我们以Gorenstein*状态为特征。我们的后者版本说，从步态策略的意义上讲，适当的分离$ \ infty $ -topos的稳定是刚性的。作为一种应用，对于分层的拓扑空间，我们阐明了这两个偶性等价之间的关系。
We discuss two known sheaf-cosheaf duality theorems: Curry's for the face posets of finite regular CW complexes and Lurie's for compact Hausdorff spaces, i.e., covariant Verdier duality. We provide a uniform formulation for them and prove their generalizations. Our version of the former works over the sphere spectrum and for more general finite posets, which we characterize in terms of the Gorenstein* condition. Our version of the latter says that the stabilization of a proper separated $\infty$-topos is rigid in the sense of Gaitsgory. As an application, for stratified topological spaces, we clarify the relation between these two duality equivalences.
