Axiomatising the dagger category of complex Hilbert spaces
Category Theory
2025-11-24 v2 Quantum Physics
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.
Keywords
Cite
@article{arxiv.2511.15410,
title = {Axiomatising the dagger category of complex Hilbert spaces},
author = {Jan Paseka and Thomas Vetterlein},
journal= {arXiv preprint arXiv:2511.15410},
year = {2025}
}
Comments
In the new version, the erroneous condition (H2) has been replaced with a weaker one. Notation has also been updated for better readability