  The Levin-Wen model of string-net condensation explains how topological
phases emerge from the microscopic degrees of freedom of a physical system.
However, the original construction is not applicable to all unitary fusion
category since some additional symmetries for the $F$-symbols are imposed. In
particular, the so-called tetrahedral symmetry is not fulfilled by many
interesting unitary fusion categories. In this paper, we present a generalized
construction of the Levin-Wen model for arbitrary multiplicity-free unitary
fusion categories that works without requiring these additional symmetries. We
explicitly calculate the matrix elements of the Hamiltonian and, furthermore,
show that it has the same properties as the original one.
