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

Categorification of Highest Weight Modules over Quantum Generalized Kac–Moody Algebras