  Let f be a degeneration of Kahler manifolds. The local invariant cycle
theorem states that for a smooth fiber of the degeneration, any cohomology
class, invariant under the monodromy action, rises from a global cohomology
class. Instead of the classical cohomology, one may consider the non-abelian
cohomology. This note demonstrates that the analogous non-abelian version of
the local invariant cycle theorem does not hold if the first non-abelian
cohomology is the moduli space (universal categorical quotient) of the
representations of the fundamental group.
