A Khovanov stable homotopy type for colored links

We extend Lipshitz and Sarkar's definition of a stable homotopy type associated to a link L whose cohomology recovers the Khovanov cohomology of L. Given an assignment c (called a coloring) of a positive integer to each component of a link L, we define a stable homotopy type X col .L c / whose cohomology recovers the c -colored Khovanov cohomology of L. This goes via Rozansky's definition of a categorified Jones-Wenzl projector P n as an infinite torus braid on n strands.