Abstract: Finite tensor categories arises in quantum groups, subfactors, planar lattice model and 2d conformal field theory. It is also been used to construct (combinatorial) quantum invariants for three-manifolds. In this talk, I will introduce the three-dimentional part of alterfold theory, which provide a topological method for studying the tensor categories. As an application, I will present a short proof of the equivalence of Reshetikhin-Turaev invariant and Turaev-Viro invariant(TQFT) for spherical fusion categories.