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arXiv · 2511.15410

Axiomatising the dagger category of complex Hilbert spaces

Jan Paseka·Thomas Vetterlein
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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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Jan Paseka, Thomas Vetterlein. 2025-11-19. Axiomatising the dagger category of complex Hilbert spaces. https://arxiv.org/abs/2511.15410

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