Khovanov homology and categorification of skein modules

For every oriented surface of finite type, we construct a functorial Khovanov homology for links in thickening the surface, which takes values categorification corresponding gl(2) skein module. The latter is mild refinement Kauffman bracket algebra, and its constructed using category foams that admits an interesting non-negative grading. We expect natural algebra structure on module can be categorified by tensor product makes link functor monoidal. candidate bifunctor target conjecture it extends to monoidal structure. This would give rise canonical basis associated verify analogue positivity Fock--Goncharov Thurston. provide evidence towards monoidality checking several instances Frohman-Gelca formula torus. Finally, recover variant Asaeda--Przytycki--Sikora homologies prove embeddings spectral sequences between them.