  We define a class of lattice models for two-dimensional topological phases
with boundary such that both the bulk and the boundary excitations are gapped.
The bulk part is constructed using a unitary tensor category $\calC$ as in the
Levin-Wen model, whereas the boundary is associated with a module category over
$\calC$. We also consider domain walls (or defect lines) between different bulk
phases. A domain wall is transparent to bulk excitations if the corresponding
unitary tensor categories are Morita equivalent. Defects of higher codimension
will also be studied. In summary, we give a dictionary between physical
ingredients of lattice models and tensor-categorical notions.
