Axioms for the category of Hilbert spaces and linear contractions

TL;DR

This paper characterizes the category of Hilbert spaces and linear contractions using elementary categorical properties, avoiding complex mathematical concepts like probabilities, norms, or dimensions.

Contribution

It provides a novel categorical axiomatization of Hilbert spaces and linear contractions based solely on elementary properties.

Findings

Categorical characterization of Hilbert spaces

Axioms do not rely on probabilities or norms

Simplifies understanding of Hilbert space structures

Abstract

The category of Hilbert spaces and linear contractions is characterised by elementary categorical properties that do not refer to probabilities, complex numbers, norm, continuity, convexity, or dimension.