  Lattice Gauge Theory in 4-dimensional Euclidean space-time is generalized to
ribbon categories which replace the category of representations of the gauge
group. This provides a framework in which the gauge group becomes a quantum
group while space-time is still given by the `classical' lattice. At the
technical level, this construction generalizes the Spin Foam Model dual to
Lattice Gauge Theory and defines the partition function for a given
triangulation of a closed and oriented piecewise-linear 4-manifold. This
definition encompasses both the standard formulation of d=4 pure Yang-Mills
theory on a lattice and the Crane-Yetter invariant of 4-manifolds. The
construction also implies that a certain class of Spin Foam Models formulated
using ribbon categories are well-defined even if they do not correspond to a
Topological Quantum Field Theory.
