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arXiv · 2605.19863

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

Ulrich Bunke
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Abstract

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

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Ulrich Bunke. 2026-05-19. $E$-theory of $X$-$C^{*}$-algebras and functor formalisms. https://arxiv.org/abs/2605.19863

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