  We present a hierarchy of quantum many-body states among which many examples
of topological order can be identified by construction. We define these states
in terms of a general, basis-independent framework of tensor networks based on
the algebraic setting of finite-dimensional Hopf C*-algebras. At the top of the
hierarchy we identify ground states of new topological lattice models extending
Kitaev's quantum double models [26]. For these states we exhibit the mechanism
responsible for their non-zero topological entanglement entropy by constructing
a renormalization group flow. Furthermore it is shown that those states of the
hierarchy associated with Kitaev's original quantum double models are related
to each other by the condensation of topological charges. We conjecture that
charge condensation is the physical mechanism underlying the hierarchy in
general.
