*Prof. Dr. Florian Girelli (University of Waterloo)*

Quantum gravity models are often built using topological models: 3d gravity is itself topological, 4d gravity can be seen as a constrained topological theory. (Quantum) groups and/or categories are the natural objects to study topological models in 3d. Instead in 4d, one expects (quantum) 2-groups and/or 2-categories to be the right tool to describe topological features in 4d. Roughly speaking, if groups can be used to decorate paths, hence defining holonomies, 2-groups can be used to decorate both paths and surfaces, hence defining both holonomies and surface holonomies (aka 2-holonomies). I will provide a general overview of the notion of Poisson/quantum 2-groups and discuss how they can provide new interesting features to build more refined quantum gravity models. In particular I will show how they can be used to define phase spaces for 3d triangulations with decorations both on the edges and the faces.