  We present a method of extracting information about topological order from
the ground state of a strongly correlated two-dimensional system represented by
an infinite projected entangled pair state (iPEPS). As in Phys. Rev. B 101,
041108 (2020) and 102, 235112 (2020) we begin by determining symmetries of the
iPEPS represented by infinite matrix product operators (iMPO) that map between
the different iPEPS transfer matrix fixed points, to which we apply the
fundamental theorem of MPS to find zipper tensors between products of iMPO's
that encode fusion properties of the anyons. The zippers can be combined to
extract topological $F$-symbols of the underlying fusion category, which
unequivocally identify the topological order of the ground state. We bring the
$F$-symbols to the canonical gauge, as well as compute the Drinfeld center of
this unitary fusion category to extract the topological $S$ and $T$ matrices
encoding mutual- and self-statistics of the emergent anyons. The algorithm is
applied to Abelian toric code, double semion and twisted quantum double of
$Z_3$, as well as to non-Abelian double Fibonacci, double Ising, and quantum
double of $S_3$ and ${\rm Rep}(S_3)$ string net models.
