$E$-theory of $X$-$C^{*}$-algebras and functor formalisms
K-Theory and Homology
2026-05-22 v2 Algebraic Topology
Operator Algebras
Abstract
We show that -theory for locally compact Hausdorff spaces constitutes a six-functor formalism which is equivalent to the six-functor formalism of -valued sheaves. We furthermore show that the -theory category for locales that can be written as unions of finite open sublocales is equivalent to the category of -valued cosheaves.
Keywords
Cite
@article{arxiv.2605.19863,
title = {$E$-theory of $X$-$C^{*}$-algebras and functor formalisms},
author = {Ulrich Bunke},
journal= {arXiv preprint arXiv:2605.19863},
year = {2026}
}
Comments
96p, small correction: (missing $A$-bilinearity condition in Prop. 5.4 added)