Signs in objective linear algebra, exemplified with exterior powers and determinants
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918398939627520 |
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| author | Kock, Joachim Møller, Jesper Michael |
| author_facet | Kock, Joachim Møller, Jesper Michael |
| contents | We develop objective linear algebra in a new setting with a cardinality functor that can take negative values. The signs arise as little homotopies, as ratios between orientations. To illustrate the workings of the theory we give an objective treatment of exterior powers and determinants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19437 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Signs in objective linear algebra, exemplified with exterior powers and determinants Kock, Joachim Møller, Jesper Michael Category Theory Algebraic Topology Combinatorics 18B10, 18B40, 05A19 We develop objective linear algebra in a new setting with a cardinality functor that can take negative values. The signs arise as little homotopies, as ratios between orientations. To illustrate the workings of the theory we give an objective treatment of exterior powers and determinants. |
| title | Signs in objective linear algebra, exemplified with exterior powers and determinants |
| topic | Category Theory Algebraic Topology Combinatorics 18B10, 18B40, 05A19 |
| url | https://arxiv.org/abs/2603.19437 |