  Group field theories are quantum field theories built on groups. They can be
seen as a tool to generate topological state-sums or quantum gravity models.
For four dimensional manifolds, different arguments have pointed towards
2-groups (such as crossed modules) as the relevant symmetry structure to probe
four dimensional topological features. Here, we introduce a group field theory
built on crossed modules which generate a four dimensional topological model,
as we prove that the Feynman diagram amplitudes can be related by Pachner
moves. This model is presumably the dual version of the Yetter-Mackaay model.
