Turaev–Viro invariants, Kitaev’s model and extended TQFTs

We will give a description of Turaev-Viro topological
quantum field theory, in particular explaining how it fits the
formalism of extended TQFTs of Baez and Lurie. We will also describe
its relation with physical models that recently became popular in
relation with quantum computing, namely Kitaev’s model and Levin-Wen
model - both of which turn out to be equivalent to a special case of
Turaev-Viro model.