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Axiomatising the dagger category of complex Hilbert spaces

2025/11/19 by Paseka, Jan, Vetterlein, Thomas
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Operator Algebra Research #Algebraic and Geometric Analysis

paper · doi:10.48550/arxiv.2511.15410

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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