nLab
Lie 3-group

Definition

A Lie 3-group of 3-Lie group is a 3-truncated ∞-group in ∞LieGrpd.

From Lie 2-crossed module

A smooth 2-crossed module is a model for semistrict Lie 3-groups, Lie Gray groups.

References

Lie 3-groups coming from Lie 2-crossed modules and morphisms from a path 3-groupoid into their delooping 3-groupoid is discussed in

• João 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)