Symmetries in QFT have a long story, involving the definition of a QFT and the characterization of its phases. A generalization of the notion of symmetry is needed to characterize some phases of QFTs, such as confinement. The generalization hinges on recognizing the topological nature of symmetry operators. With this perspective, all topological defects of a given QFT implement symmetries, even if they have no inverse. As a prime example of such non-invertible symmetries, we discuss how they can resuscitate an ABJ-anomalous symmetry. This is achieved by techniques familiar to Fractional Quantum Hall physics, and non-compact generalizations thereof.
