The construction of braided tensor categories from Hopf braces.

Let (H , ⋅ , ∘) be a Hopf brace. We first show that the category of left compatible modules over (H , ⋅ , ∘) is a tensor category. Next, we show that its Drinfeld centre is equivalent to the category H H ′ Y D of left Yetter–Drinfeld modules over (H , ⋅ , ∘) as a braided tensor category. Finally, we show that Radford's biproduct (R ♯ H , ⋅) and (R ♯ H ∘ , ∘) constitute a Hopf brace, where R is a Hopf algebra in H H ′ Y D . This presents some new method to construct Hopf braces. [ABSTRACT FROM AUTHOR]