An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.
Related 11 discussions can be seen in the recent works[246–249], and one can see its categorical interpretations
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Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
An algebraic RG formalism for topological orders uses ideals in fusion rings to encode noninvertible symmetries and condensation rules between anyons.