TY  - JOUR
T1  - Categorical isomorphisms for Hopf braces
AU  - Ramos Pérez, Brais
AU  - Fernadez Vılaboa, J.m.
AU  - Gonzalez Rodriguez, Ramon
PY  - 2025
DA  - October
Y2  - 2025
DO  - 10.15672/hujms.1511335
JF  - Hacettepe Journal of Mathematics and Statistics
PB  - Hacettepe University
WT  - DergiPark
SN  - 2651-477X
SP  - 1872
EP  - 1896
VL  - 54
IS  - 5
LA  - en
AB  - 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.
KW  - Braided monoidal category
KW  - Hopf algebra
KW  - Hopf brace
KW  - brace triple
KW  - post-Hopf algebra
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UR  - https://doi.org/10.15672/hujms.1511335
L1  - https://dergipark.org.tr/en/download/article-file/4049069
ER  -