  Gauging a global symmetry of a system amounts to introducing new degrees of
freedom whose transformation rule makes the overall system observe a local
symmetry. In quantum systems there can be obstructions to gauging a global
symmetry. When this happens the symmetry is dubbed anomalous. Such obstructions
are related to the fact that the global symmetry cannot be written as a tensor
product of local operators. In this manuscript we study non-local symmetries
that have an additional structure: they take the form of a matrix product
operator (MPO). We exploit the tensor network structure of the MPOs to
construct local operators from them satisfying the same group relations, that
is, we are able to localize even anomalous MPOs. For non-anomalous MPOs, we use
these local operators to explicitly gauge the MPO symmetry of a one-dimensional
quantum state obtaining non-trivial gauged states. We show that our gauging
procedure satisfies all the desired properties as the standard on-site case
does. We also show how this procedure is naturally represented in matrix
product states protected by MPO symmetries. In the case of anomalous MPOs, we
shed light on the obstructions to gauging these symmetries.
