An introduction to the normalized homology for the set-theoretic Yang–Baxter equation

Biracks and biquandles, which are useful for studying the knot theory, are special families of solutions to the set-theoretic Yang-Baxter equation. In 2002, a homology theory for the set-theoretic Yang-Baxter equation was introduced by Carter, Elhamdadi, and Saito.
We construct a normalized homology theory of certain set-theoretic solutions to the Yang-Baxter equation, such as cycle sets, biquandles, etc., which is a modified form of their set-theoretic Yang-Baxter homology. We, moreover, introduce homological and homotopical knot invariants obtained from the normalized homology theory.