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arXiv · 2410.05120

Manifestly unitary higher Hilbert spaces

Quan Chen·Giovanni Ferrer·Brett Hungar·David Penneys·Sean Sanford
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Abstract

Higher idempotent completion gives a formal inductive construction of the $n$-category of finite dimensional $n$-vector spaces starting with the complex numbers. We propose a manifestly unitary construction of low dimensional higher Hilbert spaces, formally constructing the $\mathrm{C}^*$-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.

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Quan Chen, Giovanni Ferrer, Brett Hungar, David Penneys, Sean Sanford. 2024-10-07. Manifestly unitary higher Hilbert spaces. https://arxiv.org/abs/2410.05120

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