∞-Lie theory

# Contents

## 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.

Revised on April 25, 2013 14:23:43 by Urs Schreiber (82.169.65.155)