Opposite brace triples, Hopf braces and matched pairs of Hopf algebras

Abstract

In this paper the category of opposite brace triples is introduced in a general braided monoidal setting. Under cocommutativity, it is proved to be isomorphic to the category of Hopf braces. Furthermore, if one considers the subcategories arising from fixing one of the underlying Hopf algebras, then these two categories are also isomorphic to the category of matched pairs over that Hopf algebra.