Lie 2-groupoid in nLab
Context
∞\infty-Lie theory
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
∞\infty-Lie groupoids
∞\infty-Lie groups
∞\infty-Lie algebroids
∞\infty-Lie algebras
Contents
Definition
A Lie 2-groupoid is a 2-truncated ∞-Lie groupoid.
Examples
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Every Lie groupoid is a special case of a Lie 2-groupoid.
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For AA an abelian Lie group, its double delooping is a Lie 2-groupoid B 2A\mathbf{B}^2 A.
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More generally for GG a Lie 2-group, its delooping BG\mathbf{B}G is a one-object lie 2-groupoid
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For XX a smooth manifold, the path 2-groupoid P 2(X)\mathbf{P}_2(X) is a Lie 2-groupoid (a 2-groupoid internal to diffeological space)s.
Last revised on April 25, 2013 at 14:23:43. See the history of this page for a list of all contributions to it.