Topological orders enriched by group symmetries are mathematically described by G-crossed braided extensions and realized in string-net models with G spins on the plaquettes. In this talk, I will outline an extension of this picture beyond group symmetries. Starting from a string-net model for anyon condensation, I show how the construction reproduces the familiar group SETO models when the input category is G-graded. When the input is not G-graded, the same lattice model still has a possibly non-invertible 0-form symmetry, generated by loops of confined anyons. The talk is based on upcoming work with Peter Huston, Kyle Kawagoe and David Penneys.