group cohomology, nonabelian group cohomology, Lie group cohomology
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
A nonabelian bundle 2-gerbe is a model for a principal 3-bundle.
The notion is
the next step in higher category theory of the notion of nonabelian bundle gerbe;
a generalization of the notion of bundle 2-gerbe from abelian to nonabelian structure 3-groups.