论文标题
分类Koszul二元性
Categorical Koszul duality
论文作者
论文摘要
在本文中，我们在DG类别和一类弯曲的煤层之间建立了Koszul二元性，从而概括了DG代数和综合弯曲煤层的相应结果。我们表明，归一化的链复合函数将准游戏和简单类别之间的quillen等效性转化为此Koszul二元性。这使我们能够对DG类别的DG神经及其伴随进行概念解释。作为一种应用，我们证明了准策略的表示类别相当于其链结核的编码类别类别。这样的推论是对分层空间上可构造的DG滑轮类别的特征，作为某个DG山结构的代码类别。
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 is equivalent to the coderived category of comodules over its chain coalgebra. 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.
