Abstract The present article represents a step forward in the study of the following problem: If A= (A₁, A₂) and H= (H₁, H₂) are Hopf braces in a symmetric monoidal category such that (A₁, H₁) and (A₂, H₂) are matched pairs of Hopf algebras, then we want to know under what conditions the pair (A₁ H₁, A₂ H₂) constitutes a new Hopf brace. We find such conditions for the pairs (A₁ H₁, A₂ H₂) and (A₁ H₁, A₂ H₂) to be Hopf braces, which are particular situations of the general problem described above, analyzing when these are cocommutative, leading to solutions to the Quantum Yang-Baxter equation. These results are applied to study when the Drinfeld’s Double gives rise to a Hopf brace.
Rodríguez et al. (Fri,) studied this question.