  We use Khovanov-Lauda-Rouquier algebras to categorify a crystal isomorphism
between a highest weight crystal and the tensor product of a perfect crystal
and another highest weight crystal, all in level 1 type A affine. The nodes of
the perfect crystal correspond to a family of trivial modules and the nodes of
the highest weight crystal correspond to simple modules, which we may also
parameterize by $\ell$-restricted partitions. In the case $\ell$ is a prime,
one can reinterpret all the results for the symmetric group in characteristic
$\ell$. The crystal operators correspond to socle of restriction and behave
compatibly with the rule for tensor product of crystal graphs.
