4 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…
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,…
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…