Gray categories with duals and their diagrams

Understand

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 strict tricategories with natural isomorphisms, and correspond directly to symmetries of the diagrams.