nLab
formal cohesive infinity-groupoid

Idea

A cohesive ∞-groupoid is formal if all its spaces of k-morphism have infinitesimal extension. If they have first order infinitesimal extension, the formal cohesive $\mathrm{\infty }$-groupoid is an ∞-Lie algebroid.

Definition

For the moment see the section Formal cohesive ∞-groupoids at cohesive (∞,1)-topos .

Examples

Special cases

A 1-truncated formal cohesive $\mathrm{\infty }$-groupoid is a formal groupoid. If the space of objects is the terminal object, this is the delooping of a formal group.

More generally, if the space of objects of a formal cohesvive $\mathrm{\infty }$-groupoid is the terminal object, it is the delooping of a formal ∞-group .