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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String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
The paper gives examples of gauging Z2 symmetries in Dijkgraaf-Witten Z2 theory and Tambara-Yamagami categories via equivariantisation, G-crossed braided zesting, and generalised orbifolds, while introducing zested orbifold data that are Morita-equivalent.
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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.
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Algebras of order parameters in one-dimensional spin systems
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.