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 (2)

• 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 (2)

• On some properties of the category of cocommutative Hopf algebras
• Groupoids and skeletal categories form a pretorsion theory in $\mathsf{Cat}$