Crystals from categorified quantum groups

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 Kashiwaraʼs 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.