Axiomatising the dagger category of complex Hilbert spaces

• URL: http://arxiv.org/abs/2511.15410v2
• Date: Fri, 21 Nov 2025 18:08:03 GMT
• Title: Axiomatising the dagger category of complex Hilbert spaces
• Authors: Jan Paseka, Thomas Vetterlein,
• Abstract summary: We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps.<n>Our axioms are chosen with the aim of an easy interpretability.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions. Our axioms are chosen with the aim of an easy interpretability: two of them describe the composition of objecs, two further ones deal with the decomposition of objects, and a final axiom expresses a symmetry property. The categorical reconstruction of complex Hilbert spaces addresses foundational issues in quantum physics. We present a simplified alternative to recent characterisations.

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