  Given a strong 2-representation of a Kac-Moody Lie algebra (in the sense of
Rouquier) we show how to extend it to a 2-representation of categorified
quantum groups (in the sense of Khovanov-Lauda). This involves checking certain
extra 2-relations which are explicit in the definition by Khovanov-Lauda and,
as it turns out, implicit in Rouquier's definition. Some applications are also
discussed.
