Manifestly unitary higher Hilbert spaces
Abstract
Abstract Higher idempotent completion gives a formal inductive construction of the ‐category of finite‐dimensional ‐vector spaces starting with the complex numbers. We propose a manifestly unitary construction of low‐dimensional higher Hilbert spaces, formally constructing the ‐3‐category of 3‐Hilbert spaces from Baez's 2‐Hilbert spaces, which itself forms a 3‐Hilbert space. We prove that the forgetful functor from 3‐Hilbert spaces to 3‐vector spaces is fully faithful but not essentially surjective.
Fields of Study & Subjects
Advanced Banach Space Theory
Holomorphic and Operator Theory
Advanced Topics in Algebra
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Publisher
- Wiley
- Volume
- 113
- Issue
- 5
- Publication date
- 1 May 2026
- Language
- EN