A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-3, author = {J. Scott Carter and Mohamed Elhamdadi and Masahico Saito}, title = {Homology theory for the set-theoretic Yang-Baxter equation and knot invariants from generalizations of quandles}, journal = {Fundamenta Mathematicae}, volume = {184}, year = {2004}, pages = {31-54}, zbl = {1067.57006}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-3} }
J. Scott Carter; Mohamed Elhamdadi; Masahico Saito. Homology theory for the set-theoretic Yang-Baxter equation and knot invariants from generalizations of quandles. Fundamenta Mathematicae, Tome 184 (2004) pp. 31-54. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm184-0-3/