Abstract
We introduce a systematic method for constructing gapped domain walls of topologically ordered systems by gauging a lower-dimensional symmetry-protected topological (SPT) order. Based on our construction, we propose a correspondence between 1d SPT phases with a non-invertible G× Rep(G)× G symmetry and invertible domain walls in the quantum double associated with the group G. We prove this correspondence when G is Abelian and provide evidence for the general case by studying the quantum double model for G=S₃. We also use our method to construct \emph{anchoring domain walls}, which are novel exotic domain walls in the 3d toric code that transform point-like excitations to semi-loop-like excitations anchored on these domain walls.