Gray categories with duals and their diagrams

Barrett JW, Meusburger C, Schaumann G (2024)

Publication Type: Journal article

Publication year: 2024

Journal

Advances in Mathematics Elsevier

Book Volume: 450

Article Number: 109740

DOI: 10.1016/j.aim.2024.109740

Abstract

The geometric and algebraic properties of Gray categories with duals are investigated by means of a diagrammatic calculus. The diagrams are three-dimensional stratifications of a cube, with regions, surfaces, lines and vertices labelled by Gray category data. These can be viewed as a generalisation of ribbon diagrams. The Gray categories present two types of duals, which are extended to functors of 2-strict tricategories with natural isomorphisms, and correspond directly to symmetries of the diagrams. It is shown that these functors can be strictified so that the symmetries of a cube are realised exactly. A new condition on Gray categories with duals called the spatial condition is defined. A class of diagrams for which the evaluation for spatial Gray categories is invariant under homeomorphisms is exhibited. This relation between the geometry of the diagrams and structures in the Gray categories proves useful in computations and has applications in topological quantum field theory.

Authors with CRIS profile

Cathérine Meusburger Professur für Mathematik (Darstellungstheorie und Mathematische Physik)

Involved external institutions

University of Nottingham GB United Kingdom (GB) Julius-Maximilians-Universität Würzburg DE Germany (DE)

How to cite

APA:

Barrett, J.W., Meusburger, C., & Schaumann, G. (2024). Gray categories with duals and their diagrams. Advances in Mathematics, 450. https://doi.org/10.1016/j.aim.2024.109740

MLA:

Barrett, John W., Cathérine Meusburger, and Gregor Schaumann. "Gray categories with duals and their diagrams." Advances in Mathematics 450 (2024).

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