  We introduce a class of 2D lattice models that describe the dynamics of
intertwiners, or, in a condensed matter interpretation, the fusion and
splitting of anyons. We identify different families and instances of
triangulation invariant, that is, topological, models inside this class. These
models give examples for symmetry protected topologically ordered 1D quantum
phases with quantum group symmetries. Furthermore the models provide
realizations for anyon condensation into a new effective vacuum. We explain the
relevance of our findings for the problem of identifying the continuum limit of
spin foam and spin net models.
