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We construct a dg-enhancement of KLRW algebras that categorifies the tensor product of a universal Verma module and several integrable irreducible modules. When the integrable modules are two-dimensional, we construct a categorical action of the blob algebra on derived categories of these dg-algebras which intertwines the categorical action of . From the above we derive a categorification of the blob algebra.
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Abel Lacabanne, Grégoire Naisse, Pedro Vaz, Tensor product categorifications, Verma modules and the blob 2-category. Quantum Topol. 12 (2021), no. 4 pp. 705–812