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...
| Autores: | , , , |
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| 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 |
| 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. |
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