Projections of Hopf braces

This paper is devoted to the study of Hopf braces projections in a monoidal setting. Given a cocommutative Hopf brace ℍ in a strict symmetric monoidal category , we define the braided monoidal category of left Yetter-Drinfeld modules over ℍ. For a Hopf brace in this category, we introduce the concep...

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Detalles Bibliográficos
Autores: Ramos Pérez, Brais, González Rodríguez, Ramón, Fernández Vilaboa, José Manuel, Rodríguez Raposo, Ana Belén
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:10347/45177
Acceso en línea:https://hdl.handle.net/10347/45177
Access Level:acceso abierto
Palabra clave:Braided monoidal categor
Hopf algebra
Hopf brace
Projection
Yetter-Drinfeld module
Descripción
Sumario:This paper is devoted to the study of Hopf braces projections in a monoidal setting. Given a cocommutative Hopf brace ℍ in a strict symmetric monoidal category , we define the braided monoidal category of left Yetter-Drinfeld modules over ℍ. For a Hopf brace in this category, we introduce the concept of bosonizable Hopf brace and we prove that its bosonization ⧓ℍ is a new Hopf brace in that gives rise to a projection of Hopf braces satisfying certain properties. Finally, taking these properties into account, we introduce the notions of v -strong projection over ℍ, =1,2,3,4, and we prove that there is a categorical equivalence between the categories of bosonizable Hopf braces in the category of left Yetter-Drinfeld modules over ℍ and the category of v4-strong projections over ℍ.