@article{article_1511335, title={Categorical isomorphisms for Hopf braces}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={54}, pages={1872–1896}, year={2025}, DOI={10.15672/hujms.1511335}, author={Fernadez Vılaboa, J.m. and Gonzalez Rodriguez, Ramon and Ramos Pérez, Brais}, keywords={Braided monoidal category, Hopf algebra, Hopf brace, brace triple, post-Hopf algebra}, abstract={In this paper, we introduce the category of brace triples in a braided monoidal setting and prove that it is isomorphic to the category of s-Hopf braces, which are a generalization of cocommutative Hopf braces. After that, we obtain a categorical isomorphism between the category of finite cocommutative Hopf braces and a certain subcategory of the category of cocommutative post-Hopf algebras, which supposes an expansion to the braided monoidal setting of the equivalence obtained for the category of vector spaces over a field $\mathbb{K}$ by Y. Li, Y. Sheng and R. Tang.}, number={5}, publisher={Hacettepe University}