Categorification of highest weight modules over quantum generalized Kac-Moody algebras

Let $U_q(\text{g})$ be a quantum generalized Kac-Moody algebra and let $V(\mathrm{\Lambda })$ be the integrable highest weight $U_q(\text{g})$-module with highest weight $\mathrm{\Lambda }$. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra $R^{\mathrm{\Lambda }}$ provides a categorification of $V(\mathrm{\Lambda })$.