Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions

• URL: http://arxiv.org/abs/2401.06584v2
• Date: Mon, 15 Jan 2024 18:37:49 GMT
• Title: Dagger categories and the complex numbers: Axioms for the category of finite-dimensional Hilbert spaces and linear contractions
• Authors: Matthew Di Meglio and Chris Heunen
• Abstract summary: We characterise the category of finite-dimensional Hilbert spaces and linear contractions using simple category-theoretics that do not refer to norms, continuity, dimension, or real numbers. Our proof directly relates limits in category theory to limits in analysis, using a new variant of the classical characterisation of the real numbers instead of Soler's theorem.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We characterise the category of finite-dimensional Hilbert spaces and linear contractions using simple category-theoretic axioms that do not refer to norms, continuity, dimension, or real numbers. Our proof directly relates limits in category theory to limits in analysis, using a new variant of the classical characterisation of the real numbers instead of Sol\`er's theorem.

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