On the semi-abelianness of cocommutative Hopf monoids
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917358278279168 |
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| author | Sciandra, Andrea Zuo, Zhenbang |
| author_facet | Sciandra, Andrea Zuo, Zhenbang |
| contents | By providing a suitable generalization of Newman's bijective correspondence known for cocommutative Hopf algebras, we prove that the category of cocommutative Hopf monoids in any abelian symmetric monoidal category is semi-abelian, once faithful (co)flatness conditions are satisfied. This result unifies and generalizes the semi-abelianness of cocommutative Hopf algebras and of cocommutative color Hopf algebras known up to now. As a consequence of the semi-abelianness, the category of cocommutative Hopf monoids is also action representable. Finally, we prove that abelian objects in the category of cocommutative Hopf monoids coincide exactly with commutative and cocommutative Hopf monoids, which form so an abelian category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_22200 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the semi-abelianness of cocommutative Hopf monoids Sciandra, Andrea Zuo, Zhenbang Category Theory Quantum Algebra Rings and Algebras Representation Theory Primary 18E13, 16T05, Secondary 18M05, 18G50 By providing a suitable generalization of Newman's bijective correspondence known for cocommutative Hopf algebras, we prove that the category of cocommutative Hopf monoids in any abelian symmetric monoidal category is semi-abelian, once faithful (co)flatness conditions are satisfied. This result unifies and generalizes the semi-abelianness of cocommutative Hopf algebras and of cocommutative color Hopf algebras known up to now. As a consequence of the semi-abelianness, the category of cocommutative Hopf monoids is also action representable. Finally, we prove that abelian objects in the category of cocommutative Hopf monoids coincide exactly with commutative and cocommutative Hopf monoids, which form so an abelian category. |
| title | On the semi-abelianness of cocommutative Hopf monoids |
| topic | Category Theory Quantum Algebra Rings and Algebras Representation Theory Primary 18E13, 16T05, Secondary 18M05, 18G50 |
| url | https://arxiv.org/abs/2603.22200 |