We study the Moore complex of a simplicial cocommutative Hopf algebra through Hopf kernels. The most striking result to emerge from this construction is the coherent definition of 2-crossed modules of cocommutative Hopf algebras. This unifies the 2-crossed module theory of groups and of Lie algebras when we take the group-like and primitive functors into consideration.
Keywords: Hopf algebra, simplicial object, Moore complex, 2-crossed module
2020 MSC: 16T05, 16S40, 18G45, 55U10, 55U15
Theory and Applications of Categories, Vol. 37, 2021, No. 7, pp 189-226.