  Simple representations of KLR algebras can be used to realize the infinity
crystal for the corresponding symmetrizable Kac-Moody algebra. It was recently
shown that, in finite and affine types, certain sub-categories of cuspidal
representations realize crystals for sub Kac-Moody algebras. Here we put that
observation an a firmer categorical footing by exhibiting a functor between the
category of representations of the KLR algebra for the sub Kac-Moody algebra
and the category of cuspidal representations of the original KLR algebra.
