Lie theory for stacky Lie groupoids


∞-Lie theory (higher geometry)


Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids




\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras


Definition: Stacky Lie groupoid

A stacky Lie groupoid (in contrast to a Lie groupoid) is an internal groupoid in the category of differentiable stacks, such that the space of objects is an ordinary manifold.

Notice that differentiable stacks are equivalent to Lie groupoids modulo Morita equivalence.


Stacky Lie groupoids and their Lie theory were introduced and studied by Chenchang Zhu and collaborators.

  • Chenchang Zhu, n-Groupoids and Stacky Groupoids, 2008, International Mathematics Research Notices (2009) 2009:4087-4141; ( arXiv:0801.2057). DOI: ( 10.1093/imrn/rnp080).

  • C.Z., Lie nn-groupoids and stacky Lie groupoids (arXiv)

  • C. Z., Lie II theorem for Lie algebroids via stacky Lie groupoids (arXiv)

  • C. Z. Lie II theorem (pdf slides)

  • Henrique Bursztyn, C.Z., Morita equivalence of Poisson manifold via stack groupoids (arXiv)

Further resources

  • nn-Café blog discussion about this is here.
Revised on November 10, 2016 23:22:14 by David Roberts (