Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909904065789952 |
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| author | Di Meglio, Matthew Heunen, Chris |
| author_facet | Di Meglio, Matthew Heunen, Chris |
| contents | We unravel a deep connection between limits of real numbers and limits in category theory. Using a new variant of the classical characterisation of the real numbers, we characterise the category of finite-dimensional Hilbert spaces and linear contractions in terms of simple category-theoretic structures and properties that do not refer to norms, continuity, or real numbers. This builds on Heunen, Kornell, and Van der Schaaf's easier characterisation of the category of all Hilbert spaces and linear contractions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions Di Meglio, Matthew Heunen, Chris Category Theory Quantum Physics We unravel a deep connection between limits of real numbers and limits in category theory. Using a new variant of the classical characterisation of the real numbers, we characterise the category of finite-dimensional Hilbert spaces and linear contractions in terms of simple category-theoretic structures and properties that do not refer to norms, continuity, or real numbers. This builds on Heunen, Kornell, and Van der Schaaf's easier characterisation of the category of all Hilbert spaces and linear contractions. |
| title | Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions |
| topic | Category Theory Quantum Physics |
| url | https://arxiv.org/abs/2401.06584 |