  We review the key steps of the construction of Levin-Wen type of models on
lattices with boundaries and defects of codimension 1,2,3 in a joint work with
Alexei Kitaev. We emphasize some universal properties, such as boundary-bulk
duality and duality-defect correspondence, shared by all these models. New
results include a detailed analysis of the local properties of a boundary
excitation and a conjecture on the functoriality of the monoidal center.
