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…
The many faces of higher Hilbert spaces
Giovanni Ferrer, Lukas Müller, David Penneys +1
Finite-dimensional operator algebras can be viewed as , , or -algebras, leading to different notions for their categories of modules and c…
The Homotopy 3-Type of Abelian C*-Algebras
Gregory Faurot, Giovanni Ferrer
We compute the homotopy groups at each unital abelian C*-algebra in the Morita -category of abelian C*-algebras, C*-algebras with central maps, C*-correspondences, and ad…
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…
Foundations for operator algebraic tricategories
Giovanni Ferrer
An operator algebraic tricategory is a higher categorical analogue of an operator algebra. For algebraic tricategories, Gordon, Power, and Street proved that every algebraic tricat…
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,…