For semisimple Lie algebra targets
For discrete group targets
For discrete 2-group targets
For Lie 2-algebra targets
For targets extending the super Poincare Lie algebra
for higher abelian targets
for symplectic Lie n-algebroid targets
FQFT and cohomology
Types of quantum field thories
Together with the Dijkgraaf-Witten model these form the first two steps in filtering of target spaces by homotopy type truncation of ∞-Chern-Simons theory with discrete target spaces. It is hence also an example of a 4d Chern-Simons theory.
The Yetter model is not the same as the Crane-Yetter model.
The Yetter-model is the ∞-Dijkgraaf-Witten theory induced by this data.
The model without a background gauge field/cocycle was considered in
The effect of having a nontrivial group 4-cocycle was considered (but now only on a 1-group) in
D. Birmingham, M. Rakowski, On Dijkgraaf-Witten Type Invariants, Lett. Math. Phys. 37 (1996), 363.
and then extended to colorings in homotopy n-types in
which has some remarks about higher (2-)group cocycles towards the end.