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The Reshetikhin-Turaev sl(N) polynomial of links colored by wedge powers ofthe defining representation has been categorified via several differentapproaches. Here, we give a concise introduction to the categorification usingmatrix factorizations, which is a direct generalization of theKhovanov-Rozansky homology. Full details of the construction are given in[arXiv:0907.0695]. We also briefly review deformations and applications of thiscategorification given in [arXiv:1002.2662, arXiv:1011.2254, arXiv:1102.0586].

Colored sl(N) link homology via matrix factorizations