nLab differential 2-crossed module

• crossed complex$\Leftarrow$ crossed module $\Rightarrow$ 2-crossed module

• dg-Lie algebra$\Leftarrow$ differential crossed module $\Rightarrow$ differential 2-crossed module

Idea

A differential 2-crossed module encodes a semistrict Lie 3-algebra in terms of a system of ordinary Lie algebras and morphisms between them. It generalizes the way a differential crossed module encodes a strict Lie 2-algebra

References

The definition is reproduced for instance in section 1.2 of

• Joao Faria Martins, Roger Picken, The fundamental Gray 3-groupoid of a smooth manifold and local 3-dimensional holonomy based on a 2-crossed module (arXiv:0907.2566)