We study the crystal structure on categories of graded modules over algebras
which categorify the negative half of the quantum Kac-Moody algebra associated
to a symmetrizable Cartan data. We identify this crystal with Kashiwara's
crystal for the corresponding negative half of the quantum Kac-Moody algebra.
As a consequence, we show the simple graded modules for certain cyclotomic
quotients carry the structure of highest weight crystals, and hence compute the
rank of the corresponding Grothendieck group.