The Moore Complex of a Simplicial Cocommutative Hopf Algebra
arXiv:1905.09620
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.
arXiv comment38 pages, final version
References in corpus (9)
- Higher-Dimensional Algebra V: 2-Groups
- A semi-abelian extension of a theorem by Takeuchi
- A torsion theory in the category of cocommutative Hopf algebras
- Pointed homotopy and pointed lax homotopy of 2-crossed module maps
- Crossed modules of Hopf algebras and of associative algebras and two-dimensional holonomy
- Transformation Double Categories Associated to 2-Group Actions
- Combinatorial categorical equivalences of Dold-Kan type
- Strict quantum 2-groups
- On some properties of the category of cocommutative Hopf algebras