论文标题
加性C*类别和K理论
Additive C*-categories and K-theory
论文作者
论文摘要
我们回顾了乘数类别的概念和$ c^{*} $类别的$ W^{*} $。然后，我们考虑$ c^{*} $类别中（可能是无限）对象的正交总和的概念。此外，我们构建了$ c^{*} $的交叉产品，包括组。我们将$ k $ - 理论的基本属性用于$ c^{*} $ - 同源函数概念中的类别。然后，我们一般研究同源函数的各种刚度属性，以及$ c^{*} $类别的$ k $ - 理论的特殊其他功能。作为一个应用程序，我们从$ c^{*} $ - 分类数据构建和研究了组轨道类别的有趣函数。
We review the notions of a multiplier category and the $W^{*}$-envelope of a $C^{*}$-category. We then consider the notion of an orthogonal sum of a (possibly infinite) family of objects in a $C^{*}$-category. Furthermore, we construct reduced crossed products of $C^{*}$-categories with groups. We axiomatize the basic properties of the $K$-theory for $C^{*}$-categories in the notion of a homological functor. We then study various rigidity properties of homological functors in general, and special additional features of the $K$-theory of $C^{*}$-categories. As an application we construct and study interesting functors on the orbit category of a group from $C^{*}$-categorical data.
