有限偏序集图表范畴之间的导出等价
Derived equivalences between diagram categories of finite posets
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中文总结 AI 辅助
本文通过引入可容许切割概念，给出了由有限偏序集索引的图表范畴间泛导出等价的构造方法，并应用于对偶、源到汇变换及树定向，同时推广到持久模块。
中文摘要 AI 辅助
我们研究由有限偏序集索引的图表范畴之间的泛导出等价。从Ladkani的一个构造出发，我们给出了一个内在判据，用于确定一个有限偏序集何时允许一个可应用该构造的分解。这引出了可容许切割的概念，该概念完全以偏序集的序结构来表述。因此，我们的主要结果提供了一种方法，从给定具有这种切割的有限偏序集出发，构造一个新的偏序集，使其与原来的偏序集泛导出等价。一旦保留划分，该构造是可逆的，从而可以从变换后的偏序集恢复原始的混合序关系。作为应用，我们证明了每个高度至多为1的有限偏序集与其对偶偏序集泛导出等价，给出了刻画在极小元素处的源到汇变换的判据，并通过一系列这样的局部变换恢复了有限树的所有定向的泛导出等价。这些结果也应用于由有限偏序集索引的持久模块以及通过附加有限参数而获得的扩展。
英文摘要
We study universal derived equivalences between diagram categories indexed by finite posets. Starting from a construction of Ladkani, we give an intrinsic criterion for determining when a finite poset admits a decomposition to which this construction can be applied. This leads to the notion of an admissible cut, formulated entirely in terms of the order structure of the poset. Our main result therefore provides a method for producing, from a given finite poset admitting such a cut, a new poset that is universally derived equivalent to it. The construction is reversible once the partition is retained, so that the original mixed order relations can be recovered from the transformed poset. As applications, we show that every finite poset of height at most one is universally derived equivalent to its opposite, give a criterion characterizing source-to-sink transformations at minimal elements, and recover the universal derived equivalence of all orientations of a finite tree through sequences of such local transformations. These results are also applied to persistence modules indexed by finite posets and to extensions obtained by adjoining further finite parameters.
发表机构
- Tampere University（坦佩雷大学）
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