∞-Lie theory (higher geometry) Background Smooth structure Higher groupoids Lie theory ∞-Lie groupoids ∞-Lie algebroids Formal Lie groupoids Cohomology Homotopy Related topics Examples -Lie groupoids -Lie groups -Lie algebroids -Lie algebras A Lie 2-groupoid is a 2-truncated ∞-Lie groupoid. Every Lie groupoid is a special case of a Lie 2-groupoid. For an abelian Lie group, its double delooping is a Lie 2-groupoid . More generally for a Lie 2-group, its delooping is a one-object lie 2-groupoid For a smooth manifold, the path 2-groupoid is a Lie 2-groupoid (a 2-groupoid internal to diffeological space)s.