Quasitriangular covariant monoidal BiHom-bialgebras, associative monoidal BiHom-Yang–Baxter equations and Rota–Baxter paired monoidal BiHom-modules
In this paper, we mainly introduce the notion of covariant monoidal BiHom-bialgebra, which is an extended form of infinitesimal monoidal BiHom-bialgebra. We focus on the characterizations of quasitriangular covariant monoidal BiHom-bialgebras, which leads to the concept of associative monoidal BiHom-Yang–Baxter pair and the associative monoidal BiHom-Yang–Baxter equation. We also investigate the relations among quasitriangular covariant monoidal BiHom-bialgebras, Rota–Baxter monoidal BiHom-systems, monoidal BiHom-pre-Lie algebras and monoidal BiHom-dendriform algebras. On the other hand, we consider Rota–Baxter paired monoidal BiHom-modules and also list some basic properties and examples of Rota–Baxter paired monoidal BiHom-modules.