# The Moore Complex of a Simplicial Cocommutative Hopf Algebra

## TL;DR

This paper develops a new framework for understanding the Moore complex of simplicial cocommutative Hopf algebras, leading to a unified theory of 2-crossed modules that bridges group and Lie algebra theories.

## Contribution

It introduces a coherent definition of 2-crossed modules of cocommutative Hopf algebras, unifying existing theories for groups and Lie algebras.

## Key findings

- Defined 2-crossed modules of cocommutative Hopf algebras.
- Unified the 2-crossed module theories of groups and Lie algebras.
- Provided a new perspective on the structure of simplicial cocommutative Hopf algebras.

## Abstract

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.

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Source: https://tomesphere.com/paper/1905.09620