  It is well-known that if we gauge a $\mathbb{Z}_n$ symmetry in two
dimensions, a dual $\mathbb{Z}_n$ symmetry appears, such that re-gauging this
dual $\mathbb{Z}_n$ symmetry leads back to the original theory. We describe how
this can be generalized to non-Abelian groups, by enlarging the concept of
symmetries from those defined by groups to those defined by unitary fusion
categories. We will see that this generalization is also useful when studying
what happens when a non-anomalous subgroup of an anomalous finite group is
gauged: for example, the gauged theory can have non-Abelian group symmetry even
when the original symmetry is an Abelian group. We then discuss the
axiomatization of two-dimensional topological quantum field theories whose
symmetry is given by a category. We see explicitly that the gauged version is a
topological quantum field theory with a new symmetry given by a dual category.
