$E$-theory of $X$-$C^{*}$-algebras and functor formalisms
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913151916703744 |
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| author | Bunke, Ulrich |
| author_facet | Bunke, Ulrich |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19863 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $E$-theory of $X$-$C^{*}$-algebras and functor formalisms Bunke, Ulrich K-Theory and Homology Algebraic Topology Operator Algebras 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. |
| title | $E$-theory of $X$-$C^{*}$-algebras and functor formalisms |
| topic | K-Theory and Homology Algebraic Topology Operator Algebras |
| url | https://arxiv.org/abs/2605.19863 |