  Fornax 4 is the most distinctive globular cluster in the Fornax dwarf
spheroidal. Located close to the centre of the galaxy, more metal-rich and
potentially younger than its four companions (namely, Fornax clusters number 1,
2, 3 and 5), it has been suggested to have experienced a different formation
than the other clusters in the galaxy. Here we use HST/WFC3 photometry to
characterize the stellar population content of this system and shed new light
on its nature. By means of a detailed comparison of synthetic horizontal branch
and red giant branch with the observed colour-magnitude diagrams, we find that
this system likely hosts stellar sub-populations characterized by a significant
iron spread up to $\Delta$[Fe/H]$\sim$0.4 dex and possibly by also some degree
of He abundance variations $\Delta$Y$\sim0.03$. We argue that this purely
observational evidence, combined with the other peculiarities characterizing
this system, supports the possibility that Fornax 4 is the nuclear star cluster
of the Fornax dwarf spheroidal galaxy. A spectroscopic follow-up for a large
number of resolved member stars is needed to confirm this interesting result
and to study in detail the formation and early evolution of this system and
more in general the process of galaxy nucleation.
