# nLab formal groupoid

Contents

### Context

#### $\infty$-Lie theory

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

## Idea

A formal groupoid is a groupoid whose hom-spaces have infinitesimal extension.

## References

The notion of formal groupoid apparently goes back to

• P. Berthelot, Cohomologie Cristalline des Schémas de Caractéristique $p \gt 0$, Springer L.N.M. 407 (1974).

and

• Luc Illusie, Complexe cotangent et déformations I , Springer L.N.M. 239 (1971); II, Springer L.N.M. 283

Formal groupoids in general and the de Rham space formal groupoid in particular are discussed also in section 7 of

Formal groupoids and their relation to Lie coalgebroids are discussed in section 1.4.15 of

The formal version of the notion of symplectic groupoids is discussed in

Last revised on April 13, 2011 at 21:53:31. See the history of this page for a list of all contributions to it.