In this paper we define the 1,2-coloured HOMFLY-PT triply graded link homology and prove that it is a link invariant. We also conjecture on how to generalize our construction for arbitrary colours.
Dos Santos Santana Forte Vaz, P., Mackaay, M., & Stosic, M. (2011). The 1,2-coloured HOMFLY-PT link homology. Transactions of the American mathematical society, 363, 2091-2124. https://doi.org/10.1090/S0002-9947-2010-05155-4 (Original work published 2011)