6 papers
Orthonormal bases for higher Hilbert spaces
Giovanni Ferrer, Brett Hungar, David Penneys +1
In our previous article [arxiv:2410.05120], we introduced the notion of a finite dimensional 3-Hilbert space, categorifying Baez's 2-Hilbert spaces. In this article, by further cat…
Anchored Planar Algebras and 3-Categorical Graphical Calculus
Brett Hungar
Anchored planar algebras, a generalized notion of Vaughan Jones' planar algebras, have recently seen use in higher category theory, functional analysis, and TQFT applications. Thes…
Manifestly unitary higher Hilbert spaces
Quan Chen, Giovanni Ferrer, Brett Hungar +2
Higher idempotent completion gives a formal inductive construction of the -category of finite dimensional -vector spaces starting with the complex numbers. We propose a manif…
Dagger -categories
Giovanni Ferrer, Brett Hungar, Theo Johnson-Freyd +8
Category theory provides a unified language for organizing composable operations in many disciplines. In disciplines where unitarity is fundamental -- such as functional analysis,…
Boundary algebras of the Kitaev Quantum Double model
Mario Tomba, Shuqi Wei, Brett Hungar +4
The recent article [arXiv:2307.12552] gave local topological order (LTO) axioms for a quantum spin system, showed they held in Kitaev's Toric Code and in Levin-Wen string net model…
Spectra of three-peg Hanoi towers graphs
Brett Hungar, Gamal Mograby, Madison Phelps +2
We consider the relationship between the Laplacians on two sequences of planar graphs, one from the theory of self-similar groups and one from analysis on fractals. By establishing…