  A family of invariants of smooth, oriented four-dimensional manifolds is
defined via handle decompositions and the Kirby calculus of framed link
diagrams. The invariants are parameterised by a pivotal functor from a
spherical fusion category into a ribbon fusion category.
  A state sum formula for the invariant is constructed via the chain-mail
procedure, so a large class of topological state sum models can be expressed as
link invariants. Most prominently, the Crane-Yetter state sum over an arbitrary
ribbon fusion category is recovered, including the nonmodular case. It is shown
that the Crane-Yetter invariant for nonmodular categories is stronger than
signature and Euler invariant.
  A special case is the four-dimensional untwisted Dijkgraaf-Witten model.
Derivations of state space dimensions of TQFTs arising from the state sum model
agree with recent calculations of ground state degeneracies in Walker-Wang
models.
  Relations to different approaches to quantum gravity such as Cartan geometry
and teleparallel gravity are also discussed.
