### A construction of the Hom-Yetter-Drinfeld category

In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter-Drinfeld category ${}_{H}^{H}$ via the Radford biproduct Hom-Hopf algebra, and prove that Hom-Yetter-Drinfeld modules can provide solutions of the Hom-Yang-Baxter equation and ${}_{H}^{H}$ is a pre-braided tensor category, where (H,β,S) is a Hom-Hopf algebra. Furthermore, we show that $(A{\u266e}_{\diamond}H,\alpha \otimes \beta )$ is a Radford biproduct Hom-Hopf algebra if and only if (A,α) is a Hom-Hopf algebra in the category ${}_{H}^{H}$. Finally,...