A colored Khovanov spectrum and its tail forB–adequate links

We define a Khovanov homotopy type for sl₂(C) colored links and quantum spin networks and derive some of its basic properties. In the case of n-colored B-adequate links, we show a stabilization of the homotopy types as the coloring n→∞, generalizing the tail behavior of the colored Jones polynomial. Finally, we also provide an alternative, simpler stabilization in the case of the colored unknot.