A Categorical and Holographic View of Symmetry

A symmetry is usually described by transformations and an associated group. However, a symmetry can also be described by the conservation of charges, encoded by their fusion rule. This leads to a description of symmetry based on fusion category. However, only  fusion categories that describe excitations of of a topological order in one higher dimension correspond to a non-trivial symmetry. In fact, the symmetry directly correspond to the topological order in one higher dimension, which leads to a holographic view of symmetry.