nLab Lie 2-groupoid

Definition

A Lie 2-groupoid is a 2-truncated ∞-Lie groupoid.

Examples

• Every Lie groupoid is a special case of a Lie 2-groupoid.

• For $A$ an abelian Lie group, its double delooping is a Lie 2-groupoid $\mathbf{B}^2 A$.

• More generally for $G$ a Lie 2-group, its delooping $\mathbf{B}G$ is a one-object lie 2-groupoid

• For $X$ a smooth manifold, the path 2-groupoid $\mathbf{P}_2(X)$ is a Lie 2-groupoid (a 2-groupoid internal to diffeological space)s.

Related concepts

• double Lie algebroid, Lie algebroid-groupoid, double Lie groupoid

• higher differential geometry

  • smooth infinity-groupoid

Literatur

• M. Jotz, L. Mußmächer: Three explicit examples of Lie 2-groupoids [arXiv:2608.17811]