We give the crystal structure of the Grothendieck group G₀(R) of irreducible modules over the quiver Hecke algebra R constructed in {TW2023}. This leads to the categorification of the crystal B(∞) of the quantum Borcherds algebra Uq( g) and its irreducible highest weight crystal B(λ) for arbitrary Borcherds-Cartan data. Additionally, we study the cyclotomic categorification of irreducible highest weight Uq( g)-modules.
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Tong et al. (2024) studied this question.
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