半单张量范畴与模范畴的导出重构

中文摘要 AI 辅助

我们研究了半单张量范畴及其半单模范畴的有界导出范畴。这些范畴可能具有无穷多个简单同构类。我们通过普遍分次群的整值特征与整数偏差对有界幺半$t$-结构进行分类。我们还利用模分量的稳定化子子群对相容的模$t$-结构进行分类。相应的心与原始范畴是张量等价和模等价的。由此可知，幺半导出等价和相容导出模等价能够同时恢复张量范畴及其模范畴。

英文摘要

We study bounded derived categories of semisimple tensor categories and their semisimple module categories. These categories may have infinitely many simple isomorphism classes. We classify bounded monoidal $t$-structures by integer-valued characters of the universal grading group and an integer deviation. We also classify compatible module $t$-structures using stabilizer subgroups of the module components. The corresponding hearts are tensor and module equivalent to the original categories. It follows that a monoidal derived equivalence and a coherent derived module equivalence recover both the tensor category and its module category.

发表机构

• Capital Normal University（首都师范大学）

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