  The classical double copy relates exact solutions in biadjoint scalar, gauge
and gravity theories. Recently, nonperturbative solutions have been found in
biadjoint theory, which have been speculated to be related to the Wu-Yang
monopole in gauge theory. We show that this seems not to be the case, by
considering monopole solutions in the infinitely boosted (shockwave) limit.
Furthermore, we show that the Wu-Yang monopole is instead related to the
Taub-NUT solution, whose previously noted single copy is that of an
abelian-like (Dirac) monopole. Our results demonstrate how abelian and
non-abelian gauge theory objects can be associated with the same gravity
object, and clarify a number of open questions concerning the scope of the
classical double copy.
