Any weakly integral fusion category admits a QCA-refined realization on tensor-product Hilbert spaces with QCA and symmetry indices fixed by the categorical data under defect assumptions.
On the classification of weakly integral modular categories
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Non-Invertible Symmetries on Tensor-Product Hilbert Spaces and Quantum Cellular Automata
Any weakly integral fusion category admits a QCA-refined realization on tensor-product Hilbert spaces with QCA and symmetry indices fixed by the categorical data under defect assumptions.