par Gran, Marino;Sterck, Florence 
;Vercruysse, Joost
Référence Journal of pure and applied algebra, 223, 10, page (4171-4190)
Publication Publié, 2019-10-01
;Vercruysse, Joost Référence Journal of pure and applied algebra, 223, 10, page (4171-4190)
Publication Publié, 2019-10-01
Article révisé par les pairs
| Résumé : | We prove that the category of cocommutative Hopf algebras over a field is a semi-abelian category. This result extends a previous special case of it, based on the Milnor–Moore theorem, where the field was assumed to have zero characteristic. Takeuchi's theorem asserting that the category of commutative and cocommutative Hopf algebras over a field is abelian immediately follows from this new observation. We also prove that the category of cocommutative Hopf algebras over a field is action representable. We make some new observations concerning the categorical commutator of normal Hopf subalgebras, and this leads to the proof that two definitions of crossed modules of cocommutative Hopf algebras are equivalent in this context. |
