Localization of Cofibration Categories and Groupoid $C^*$-algebras
Algebraic Topology
2018-03-16 v1 Category Theory
K-Theory and Homology
Operator Algebras
Abstract
We prove that relative functors out of a cofibration category are essentially the same as relative functors which are only defined on the subcategory of cofibrations. As an application we give a new construction of the functor that assigns to a groupoid its groupoid -algebra and thereby its topological -theory spectrum.
Keywords
Cite
@article{arxiv.1609.03805,
title = {Localization of Cofibration Categories and Groupoid $C^*$-algebras},
author = {Markus Land and Thomas Nikolaus and Karol Szumiło},
journal= {arXiv preprint arXiv:1609.03805},
year = {2018}
}