Categorical Koszul duality
Categorical Koszul duality
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DOI：
10.1016/j.aim.2022.108644
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发表时间：
2020-06
影响因子：
1.7
通讯作者：
Julian V. S. Holstein;A. Lazarev
中科院分区：
文献类型：
--
作者：
Julian V. S. Holstein;A. Lazarev
在本文中，我们建立了 dg 类别和一类弯曲余代数之间的 Koszul 对偶性，推广了 dg 代数和共能弯曲余代数的相应结果。我们证明了归一化链复函子将准范畴和单纯范畴之间的 Quillen 等价转化为 Koszul 对偶性。这使我们能够对 dg 范畴及其伴随物的 dg 神经给出概念性解释。作为一个应用，我们证明准范畴 K 的表示范畴等价于 K 的链余代数 C⁎(K) 上余模的协导出范畴。其推论是将分层空间上的可构造 dg 滑轮范畴表征为某个 dg 余代数的协导出范畴。
In this paper we establish Koszul duality between dg categories and a class of curved coalgebras, generalizing the corresponding result for dg algebras and conilpotent curved coalgebras. We show that the normalized chain complex functor transforms the Quillen equivalence between quasicategories and simplicial categories into this Koszul duality. This allows us to give a conceptual interpretation of the dg nerve of a dg category and its adjoint. As an application, we prove that the category of representations of a quasicategory K is equivalent to the coderived category of comodules over C⁎(K), the chain coalgebra of K. A corollary of this is a characterization of the category of constructible dg sheaves on a stratified space as the coderived category of a certain dg coalgebra.