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We study the Moore complex of a simplicial cocommutative Hopf algebra throughHopf kernels. The most striking result to emerge from this construction is thecoherent definition of 2-crossed modules of cocommutative Hopf algebras. Thisunifies the 2-crossed module theory of groups and of Lie algebras when we takethe group-like and primitive functors into consideration.

The Moore Complex of a Simplicial Cocommutative Hopf Algebra