Key points are not available for this paper at this time.
The authors provide a comprehensive study of the role of boundary conditions in the presence of generalized non-invertible symmetries, beginning with the question of when boundary conditions are symmetric under those symmetries. They find different categories of symmetric boundary conditions (which would be identical under normal symmetries) and discuss their relation to 't Hooft anomalies, gauging, and RG flows.
Choi et al. (Mon,) studied this question.