  In the Standard Model, some combination of the baryon $\bf B$ and lepton $\bf
L$ number symmetry is free of mixed anomalies with strong and electroweak
$su(3) \times su(2) \times u(1)_{\tilde Y}$ gauge forces. However, it can still
suffer from a mixed gravitational anomaly, hypothetically pertinent to
leptogenesis in the very early universe. This happens when the total "sterile
right-handed" neutrino number $n_{\nu_R}$ is not equal to the family number
$N_f$. Thus the invertible $\bf B - L$ symmetry current conservation can be
violated quantum mechanically by gravitational backgrounds such as
gravitational instantons. In specific, we show that a noninvertible categorical
$\bf B - L$ generalized symmetry still survives in gravitational backgrounds.
In general, we propose a construction of noninvertible symmetry charge
operators as topological defects derived from invertible anomalous symmetries
that suffer from mixed gravitational anomalies. Examples include the
perturbative local and nonperturbative global anomalies classified by
$\mathbb{Z}$ and $\mathbb{Z}_{16}$ respectively. For this construction, we
utilize the anomaly inflow bulk-boundary correspondence, the 4d Pontryagin
class and the gravitational Chern-Simons 3-form, the 3d
Witten-Reshetikhin-Turaev-type topological quantum field theory corresponding
to a 2d rational conformal field theory with an appropriate rational chiral
central charge, and the 4d $\mathbb{Z}_4^{\rm TF}$-time-reversal symmetric
topological superconductor with 3d boundary topological order.
