We have shown that the mathematical structures in a recent work of Bultinck-Mariena-Williamson-Sahinoglu-Haegeman-Verstraete are the same as those of flat symmetric bi-unitary connections and the tube algebra in subfactor theory. More specifically, a system of flat symmetric bi-unitary connections arising from a subfactor with finite index and finite depth satisfies all their requirements for tensors and the tube algebra for such a subfactor and the anyon algebra for such tensors are isomorphic up to the normalization constants. The Verlinde formula follows from this identification.