2020/10/28 by Bunke, Ulrich, Engel, Alexander
#Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.2010.14830
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.