Higher-group symmetry in lattice gauge theories with restricted topological sectors

In this paper, we give a brief overview of generalized symmetries from the point of view of the lattice regularization as a fully regularized framework. At first, we illustrate the generalization of 't~Hooft anomaly matching for higher-form symmetries. Furthermore the main interest goes to the higher-group symmetry. In particular, we find that the so-called $4$-group appears in the lattice Yang--Mills theory under modification of instanton sum.