A remark on the invariance of $K$-theory under duality
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914379946000384 |
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| author | Lehner, Georg |
| author_facet | Lehner, Georg |
| contents | In this short remark, we explain that two examples of invariance under duality for a localizing invariant $F$ hold purely formally when $F$ is $K$-theory, whereas the general statement for arbitrary localizing invariants does not reduce to a formal statement. We record a counterexample to the claim that the universal localizing invariant is invariant under the operation of taking opposite categories, originally due to Tabuada. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08344 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A remark on the invariance of $K$-theory under duality Lehner, Georg K-Theory and Homology Algebraic Topology Primary: 19D99, 18F25, Secondary: 18N60, 18F20, 16K50 In this short remark, we explain that two examples of invariance under duality for a localizing invariant $F$ hold purely formally when $F$ is $K$-theory, whereas the general statement for arbitrary localizing invariants does not reduce to a formal statement. We record a counterexample to the claim that the universal localizing invariant is invariant under the operation of taking opposite categories, originally due to Tabuada. |
| title | A remark on the invariance of $K$-theory under duality |
| topic | K-Theory and Homology Algebraic Topology Primary: 19D99, 18F25, Secondary: 18N60, 18F20, 16K50 |
| url | https://arxiv.org/abs/2603.08344 |