Can locality survive non-invertible symmetries on lattices?

Physicists study how locality principles (Haag duality and disjoint additivity) behave in 2+1D lattice systems with non-invertible symmetries governed by Hopf algebras. They find that Haag duality holds exactly only for regions without sharp corners; cusped regions require a boundary collar to restore the principle. The results apply to string-net models and lattice gauge theories, establishing when the algebra of local operators remains sensible.