On some properties of the category of cocommutative Hopf Algebras

Abstract

By a recent work of Gran-Kadjo-Vercruysse, the category of cocommutative Hopf algebras over a field of characteristic zero is semi-abelian. In this paper, we explore some properties of this category, in particular we show that its abelian core is the category of commutative and cocommutative Hopf algebras.