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In this paper, we introduce the category of brace triples in a braidedmonoidal setting and prove that it is isomorphic to the category of s-Hopfbraces, which are a generalization of cocommutative Hopf braces. After that, weobtain a categorical isomorphism between finite cocommutative Hopf braces and acertain subcategory of cocommutative post-Hopf algebras, which suppose anexpansion to the braided monoidal setting of the equivalence obtained by Y. Li,Y. Sheng and R. Tang for the category of vector spaces over a field$\mathbb{K}$.

Categorical isomorphisms for Hopf braces