Categorical isomorphisms for Hopf braces

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 cocommutat...

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Detalles Bibliográficos
Autores: Ramos Pérez, Brais, Fernández Vilaboa, José Manuel, González Rodríguez, Ramón
Tipo de recurso: artículo
Fecha de publicación:2025
País:España
Institución:Universidad de Santiago de Compostela (USC)
Repositorio:Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela
Idioma:inglés
OAI Identifier:oai:minerva.usc.gal:10347/45217
Acceso en línea:https://hdl.handle.net/10347/45217
Access Level:acceso abierto
Palabra clave:Braided monoidal category
Hopf algebra
Hopf brace
Brace triple
Post-Hopf algebra
Descripción
Sumario: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 K by Y. Li, Y. Sheng and R. Tang.