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arXiv · 2402.18228

$E$-theory is compactly assembled

Ulrich Bunke·Benjamin Duenzinger
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Abstract

We show that the equivariant $E$-theory category $\mathrm{E}_{\mathrm{sep}}^{G}$ for separable $C^{*}$-algebras is a compactly assembled stable $\infty$-category. We derive this result as a consequence of the shape theory for $C^{*}$-algebras developed by Blackadar and Dardarlat and a new construction of $\mathrm{E}_{\mathrm{sep}}^{G}$. As an application we investigate a topological enrichment of the homotopy category of a compactly assembled $\infty$-category in general and argue that the results of Carrión and Schafhauser on the enrichment of the classical $E$-theory category can be derived by specialization.

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Ulrich Bunke, Benjamin Duenzinger. 2025-03-28. $E$-theory is compactly assembled. https://arxiv.org/abs/2402.18228

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