Categorical isomorphisms for Hopf braces

Year 2025, Volume: 54 Issue: 5, 1872 - 1896, 29.10.2025

J.m. Fernadez Vılaboa , Ramon Gonzalez Rodriguez , Brais Ramos Pérez

https://doi.org/10.15672/hujms.1511335

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.

Keywords

Braided monoidal category , Hopf algebra , Hopf brace , brace triple , post-Hopf algebra

Project Number

PID2020-115155GB-I00

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