Categorical isomorphisms for Hopf braces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866912322805563392 |
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| author | Vilaboa, José Manuel Fernández Rodríguez, Ramón González Pérez, Brais Ramos |
| author_facet | Vilaboa, José Manuel Fernández Rodríguez, Ramón González Pérez, Brais Ramos |
| contents | 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 finite cocommutative Hopf braces and a certain subcategory of cocommutative post-Hopf algebras, which suppose an expansion to the braided monoidal setting of the equivalence obtained by Y. Li, Y. Sheng and R. Tang for the category of vector spaces over a field $\mathbb{K}$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_05235 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Categorical isomorphisms for Hopf braces Vilaboa, José Manuel Fernández Rodríguez, Ramón González Pérez, Brais Ramos Rings and Algebras 18M05, 16T05 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 finite cocommutative Hopf braces and a certain subcategory of cocommutative post-Hopf algebras, which suppose an expansion to the braided monoidal setting of the equivalence obtained by Y. Li, Y. Sheng and R. Tang for the category of vector spaces over a field $\mathbb{K}$. |
| title | Categorical isomorphisms for Hopf braces |
| topic | Rings and Algebras 18M05, 16T05 |
| url | https://arxiv.org/abs/2311.05235 |