Abstract
We show that Khovanov homology (and its sl3 variant) can be understood in the context of higher representation theory. Specifically, we show that the combinatorially defined foam constructions of these theories arise as a family of 2ârepresentations of categorified quantum slm via categorical skew Howe duality. Utilizing Cautisâ Rozansky categorified clasps we also obtain a unified construction of foam-based categorifications of JonesâWenzl projectors and their sl3 analogs purely from the higher representation theory of categorified quantum groups. In the sl2 case, this work reveals the importance of a modified class of foams introduced by Christian Blanchet which in turn suggest a similar modified version of the sl3 foam category introduced here. 81R50; 17B37, 57M25, 18G60
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