Dagger Categories and the Complex Numbers: Axioms for the Category of Finite-Dimensional Hilbert Spaces and Linear Contractions
Year: 2025
Type: article
Abstract: We unravel a deep connection between limits of real numbers and limits in category theory. Using a new variant of the classical characterisation of the real numbers, we characterise the category of finite-dimensional Hilbert spaces and linear contractions in terms of simple category-theoretic structures and properties that do not refer to norms, continuity, or real numbers. This builds on Heunen, Kornell, and Van der Schaaf’s easier characterisation of the category of all Hilbert spaces and linear contractions.
Source: Applied Categorical Structures
Authors: Matthew Di Meglio, Chris Heunen
Institution: University of Edinburgh
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4410739305