Solutions of Hom-Yang–Baxter Equation from Monoidal Hom-(Co)Algebra Structures

A method for constructing solutions of the Hom-Yang–Baxter equations is presented. Thus methods yields a so-called $\alpha$-involutory solution of the Hom-Yang–Baxter equation for every monoidal Hom-(co)algebra structure on a space. Characterizations for solutions of Hom-Yang–Baxter equations arising from monoidal Hom-(co)algebra structures are given, and a monoidal Hom-(co)algebra structure which produces such a solution is constructed.