For non-invertible on-site symmetries on 2+1D lattices, Haag duality is preserved exactly only for cuspless regions (weak form with collar for cusped regions); disjoint additivity holds for group-based double models and is weakened for general Hopf algebra constraints, including extended string-net
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Algebraic locality and non-invertible Gauss laws
For non-invertible on-site symmetries on 2+1D lattices, Haag duality is preserved exactly only for cuspless regions (weak form with collar for cusped regions); disjoint additivity holds for group-based double models and is weakened for general Hopf algebra constraints, including extended string-net