A Colored Khovanov Homotopy Type For Links, And Its Tail For The Unknot

In a previous paper, the author showed that the Khovanov homotopy types of the torus links $T(n,m)$ stabilize as $m\rightarrow\infty$. In this sequel, we use similar techniques to extend this result in two directions. First, we construct a stable colored version of the Khovanov homotopy type whose reduced cohomology recovers the colored Khovanov homology of the link. Second, in the case of the $T(n,\infty)$ as above, we show a further stabilization as $n\rightarrow\infty$.