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A semi-abelian extension of a theorem by Takeuchi. (English) Zbl 1440.18013

Authors’ abstract: We prove that the category of cocommutative Hopf algebras over a field is a semiabelian 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 inmediately follows from this new observation.

MSC:

18E10 Abelian categories, Grothendieck categories
18G50 Nonabelian homological algebra (category-theoretic aspects)
16T05 Hopf algebras and their applications
16B50 Category-theoretic methods and results in associative algebras (except as in 16D90)
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)
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