  We study systems with an Adler-Bell-Jackiw anomaly in terms of non-invertible
symmetry. We present a new kind of non-invertible charge defect where a key
role is played by a local current operator localized on the defect. The charge
defects are now labeled by elements of a continuous $U(1)$. We use this
construction to prove an analogue of Goldstone's theorem for such
non-invertible symmetries. We comment on possible applications to string
theory.
