A toy model for categorical charges

We consider a higher gauge topological model in three spatial dimensions whose input datum is a 2-group encoding the mixing of a 0-form $\mathbb Z_2$- and 1-form $\mathbb Z_3$-symmetry. We study the excitation content of the theory on the symmetry-preserving boundary. We show that boundary operators are organised into the fusion 2-category of 2-representations of the 2-group. These can be interpreted as categorical charges for an effective boundary model that inherits a global 2-group symmetry from the bulk topological order. Interestingly, we find that certain simple 2-representations are physically interpreted as composites of intrinsic excitations and condensation defects.