$E$-theory is compactly assembled
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917969280368640 |
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| author | Bunke, Ulrich Duenzinger, Benjamin |
| author_facet | Bunke, Ulrich Duenzinger, Benjamin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18228 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $E$-theory is compactly assembled Bunke, Ulrich Duenzinger, Benjamin K-Theory and Homology Algebraic Topology Operator Algebras 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. |
| title | $E$-theory is compactly assembled |
| topic | K-Theory and Homology Algebraic Topology Operator Algebras |
| url | https://arxiv.org/abs/2402.18228 |