论文标题
$ \ mathrm {k} $的本地化定理 - 稳定的$ \ infty $ - 类别
The localisation theorem for the $\mathrm{K}$-theory of stable $\infty$-categories
论文作者
论文摘要
我们为代数$ \ mathrm {k} $的本地化和辅助定理提供了一个相当独立的说明 - 稳定的$ \ infty $ - 类别的理论。它基于一个通用公式，用于在Waldhausen的工作后紧密地在Verdier商上评估添加剂函子。我们还包括$ \ mathrm {k} $ - 理论的添加性定理的新证明，其强烈的启发是由Ranicki的代数Thom Construction启发，这是Blumberg，Gepner和Tabuada的普遍性的简短证明，并证明了辅助定理可以单独衍生出cofinatity shore the Cofinatity holy of Universal属性。
We provide a fairly self-contained account of the localisation and cofinality theorems for the algebraic $\mathrm{K}$-theory of stable $\infty$-categories. It is based on a general formula for the evaluation of an additive functor on a Verdier quotient closely following work of Waldhausen. We also include a new proof of the additivity theorem of $\mathrm{K}$-theory, strongly inspired by Ranicki's algebraic Thom construction, a short proof of the universality theorem of Blumberg, Gepner and Tabuada, and demonstrate that the cofinality theorem can be derived from the universal property alone.
