The 1,2-coloured HOMFLY-PT link homology
  In this paper we define the 1,2-coloured HOMFLY-PT link homology and prove that it is a link invariant. We conjecture that this homology categorifies the coloured HOMFLY-PT polynomial for links whose components are labelled 1 or 2. 
Marco Mackaay, Marko Stosic and Pedro Vaz