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Let (H, β) be a Hom-bialgebra such that β2 = idH. (A, αA) is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category HH YD and (B, αB) is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category YD HH . The authors define the two-sided smash product Hom-algebra $$\left( {A\natural H\natural B,{\alpha _A} \otimes \beta \otimes {\alpha _B}} \right)$$ ( A ♮ H ♮ B , α A ⊗ β ⊗...
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