nLab formal groupoid

Idea

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

Related concepts

• A formal groupoid over the point if the delooping of a formal group.

• The ∞-groupoid-notion of formal groupoids is discussed at formal cohesive ∞-groupoid .

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

• Carlos Simpson, The Hodge filtration on nonabelian cohomology (arXiv:alg-geom/9604005)

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

• Alexander Beilinson, Vladimir Drinfeld, Chiral Algebras

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

• Alberto Cattaneo, Benoit Dherin, Giovanni Felder, Formal symplectic groupoid (arXiv:0312380)