We study the skein relation that governs the HOMFLYPT invariant of links colored by one-column Young diagrams. Our main result is a categorification of this colored skein relation. This takes the form of a homotopy equivalence between two one-sided twisted complexes constructed from Rickard complexes of singular Soergel bimodules associated to braided webs. Along the way, we prove a conjecture of Beliakova–Habiro relating the colored 2-strand full twist complex with the categorical ribbon element for quantum sl₂.
Hogancamp et al. (Tue,) studied this question.