  Levin-Wen models are a class of two-dimensional lattice spin models with a
Hamiltonian that is a sum of commuting projectors, which describe topological
phases of matter related to Drinfeld centres. We generalise this construction
to lattice systems internal to a topological phase described by an arbitrary
modular fusion category $\mathcal{C}$. The lattice system is defined in terms
of an orbifold datum $\mathbb{A}$ in $\mathcal{C}$, from which we construct a
state space and a commuting-projector Hamiltonian $H_{\mathbb{A}}$ acting on
it. The topological phase of the degenerate ground states of $H_{\mathbb{A}}$
is characterised by a modular fusion category $\mathcal{C}_{\mathbb{A}}$
defined directly in terms of $\mathbb{A}$. By choosing different $\mathbb{A}$'s
for a fixed $\mathcal{C}$, one obtains precisely all phases which are
Witt-equivalent to $\mathcal{C}$.
  As special cases we recover the Kitaev and the Levin-Wen lattice models from
instances of orbifold data in the trivial modular fusion category of vector
spaces, as well as phases obtained by anyon condensation in a given phase
$\mathcal{C}$.
