Opposite brace triples form a category isomorphic to Hopf braces under cocommutativity and to matched pairs of Hopf algebras in fixed subcategories.
Schauenburg, On the braiding on a Hopf algebra in a braided category,New York J
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Opposite brace triples, Hopf braces and matched pairs of Hopf algebras
Opposite brace triples form a category isomorphic to Hopf braces under cocommutativity and to matched pairs of Hopf algebras in fixed subcategories.