A Kirby color for Khovanov homology

We construct a Kirby color in the setting of Khovanov homology: an ind-object of the annular Bar-Natan category that is equipped with a natural handle slide isomorphism. Using functoriality and cabling properties of Khovanov homology, we define a Kirby-colored Khovanov homology that is invariant under the handle slide Kirby move, up to isomorphism. Via the Manolescu–Neithalath 2-handle formula, Kirby-colored Khovanov homology agrees with the ${\mathfrak{g}\mathfrak{l}}_2$ skein lasagna module, hence is an invariant of $4$-dimensional $2$-handlebodies.