论文标题
单相OO类别中的相对张量产品和koszul二元性
Relative tensor products and Koszul duality in monoidal oo-categories
论文作者
论文摘要
这项半阶梯性工作涵盖了在高代数中开发的相对张量产物理论的中心方面，以及它们在单型OO类别中代数的Koszul二元性中的应用。我们目标的一部分是扩展LOC的相当冷凝的帐户。引用一路上，我们概括了理论的各个方面。例如，给定一个单体OO类别CC，一个在CC上左填充的OO类别MM和CC中的代数A，我们构建了A-A-A-Bimodules N在CC中的作用，左A模块MM中MM中的A-A-Modules M在MM中由“外部相对张力”均出现“ N \ otimes_a M. 文学。 作为应用程序，我们概括了LOC的Koszul二元性。引用包括模块。我们直接的方法要求我们在这一点上假设张量产品和极限之间的某些兼容性。 Brantner，Campos和Nuiten（Arxiv：2104.03870）最近已证明这些假设在工作中是不必要的。
This semi-expository work covers central aspects of the theory of relative tensor products as developed in Higher Algebra, as well as their application to Koszul duality for algebras in monoidal oo-categories. Part of our goal is to expand on the rather condensed account of loc. cit. Along the way, we generalize various aspects of the theory. For instance, given a monoidal oo-category Cc, an oo-category Mm which is left-tensored over Cc, and an algebra A in Cc, we construct an action of A-A-bimodules N in Cc on left A-modules M in Mm by an "external relative tensor product" N \otimes_A M. (Up until now, even the special ("internal") case Cc = Mm appears to have escaped the literature. As an application, we generalize the Koszul duality of loc. cit. to include modules. Our straightforward approach requires that we at this point assume certain compatibilities between tensor products and limits; these assumptions have recently been shown to be unnecessary in work by Brantner, Campos and Nuiten (arXiv:2104.03870).
