A torsion theory in the category of cocommutative Hopf algebras

Abstract

The purpose of this article is to prove that the category of cocommutative Hopf $K$-algebras, over a field $K$ of characteristic zero, is a semi-abelian category. Moreover, we show that this category is action representable, and that it contains a torsion theory whose torsion-free and torsion parts are given by the category of groups and by the category of Lie $K$-algebras, respectively.

References in corpus (4)

• Protoadditive functors, derived torsion theories and homology
• On epimorphisms and monomorphisms of Hopf algebras
• A description of the fundamental group in terms of commutators and closure operators
• On some properties of the category of cocommutative Hopf algebras

Cited by in corpus (11)

• A semi-abelian extension of a theorem by Takeuchi
• A characterisation of Lie algebras amongst anti-commutative algebras
• A note on split extensions of bialgebras
• On some properties of the category of cocommutative Hopf algebras
• Semi-localizations of semi-abelian categories
• Groupoids and skeletal categories form a pretorsion theory in $\mathsf{Cat}$
• Split extension classifiers in the category of cocommutative Hopf algebras
• Some remarks on protolocalizations and protoadditive reflections
• Split extensions and actions of bialgebras and Hopf algebras
• The Zassenhaus lemma in star-regular categories
• The Moore Complex of a Simplicial Cocommutative Hopf Algebra