  A bi-unitary connection in subfactor theory of Jones producing a subfactor of
finite depth gives a 4-tensor appearing in a recent work of
Bultinck-Mariena-Williamson-Sahinoglu-Haegemana-Verstraete on 2-dimensional
topological order and anyons. In their work, they have a special projection
called a projector matrix product operator. We prove that the range of this
projection of length k is naturally identified with the k-th higher relative
commutant of the subfactor arising from the bi-unitary connection. This gives a
further connection between 2-dimensional topological order and subfactor
theory.
