Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.
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Constructs Z_N extended fusion rings and modular partition functions for nonanomalous subgroups, extending to multicomponent systems and orbifoldings in CFTs.
Framework using smeared boundary CFTs classifies gapped phases dual to massless RG flows, showing they often spontaneously break non-group-like symmetries via unusual module structures outside standard boundary critical phenomena.
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Topological lattice gauge theory enriched by non-invertible symmetry
Condensing an arbitrary algebra of charges in a quantum double model yields a hypergroup-graded extension of the deconfined excitations category whose domain walls act non-invertibly via a Hopf monad.