论文标题
koszul himoids中的类别类别
Koszul Monoids in Quasi-abelian Categories
论文作者
论文摘要
假设我们有一个封闭的对称单型准阿贝尔类别$ \ mathcal {e} $，带有足够平坦的投影剂，例如完整的出生空间的类别$ \ textbf {cborn} _k $或Banach Space Spaces $ \ textbf $ \ textbf $ \ textbf $ \ textbf $ \ fextbf {indban} ___的归纳限制类别。在$ \ Mathcal {e} $中与Monoids合作，我们可以概括并扩展贝林森，金兹堡，苏格尔的Koszul双重理论。我们使用一种无元素的方法来定义Koszul单体的概念，以及二次的单体及其双重。施耐德（Schneiders）将准阿贝尔类别嵌入到一个阿贝尔类别中，左心心脏，使我们能够证明比等于koszul monoids及其双重模块的派生类别的某些子类别。
Suppose that we have a bicomplete closed symmetric monoidal quasi-abelian category $\mathcal{E}$ with enough flat projectives, such as the category of complete bornological spaces $\textbf{CBorn}_k$ or the category of inductive limits of Banach spaces $\textbf{IndBan}_k$. Working with monoids in $\mathcal{E}$, we can generalise and extend the Koszul duality theory of Beilinson, Ginzburg, Soergel. We use an element-free approach to define the notions of Koszul monoids, and quadratic monoids and their duals. Schneiders' embedding of a quasi-abelian category into an abelian category, its left heart, allows us to prove an equivalence of certain subcategories of the derived categories of graded modules over Koszul monoids and their duals.
