I will explain how to categorically generalize the usual notion of symmetry to that of higher symmetry, in terms of V-local fusion n-category. I will then discuss how to characterize topological phases with a given higher symmetry, a.k.a. higher SET. The first piece of data is the fusion n-category of topological defects, which contains the V-local fusion n-category. Then one considers the center, physically the bulk. A nontrivial bulk indicates anomaly. Thus the second piece of data is the equivalence functor from the trivial bulk, namely the center of the V-local fusion n-category, to the bulk of the higher SET. One can then categorically gauge the higher SET.