  We study a family of non-Abelian topological models in a lattice that arise
by modifying the Kitaev model through the introduction of single-qudit terms.
The effect of these terms amounts to a reduction of the discrete gauge symmetry
with respect to the original systems, which corresponds to a generalized
mechanism of explicit symmetry breaking. The topological order is either
partially lost or completely destroyed throughout the various models. The new
systems display condensation and confinement of the topological charges present
in the standard non-Abelian Kitaev models, which we study in terms of ribbon
operator algebras.
