English

$E$-theory of $X$-$C^{*}$-algebras and functor formalisms

K-Theory and Homology 2026-05-22 v2 Algebraic Topology Operator Algebras

Abstract

We show that EE-theory for locally compact Hausdorff spaces constitutes a six-functor formalism which is equivalent to the six-functor formalism of E\mathrm{E}-valued sheaves. We furthermore show that the EE-theory category for locales that can be written as unions of finite open sublocales is equivalent to the category of E\mathrm{E}-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)