  The Adler-Bell-Jackiw anomaly determines the violation of chiral symmetry
when massless fermions are coupled to an abelian gauge field. In its seminal
paper, Adler noticed that a modified chiral U(1) symmetry could still be
defined, at the expense of being generated by a non-gauge-invariant conserved
current. We show this internal U(1) symmetry has the special feature that it
transforms the Haag duality violating sectors (or non local operator classes).
This provides a simple unifying perspective on the origin of anomaly
quantization, anomaly matching, applicability of Goldstone theorem, and the
absence of a Noether current. We comment on recent literature where this
symmetry is considered to be either absent or non-invertible. We end by
recalling the DHR reconstruction theorem, which states 0-form symmetries cannot
be non-invertible for d>2, and argue for a higher form-symmetry reconstruction
theorem.
