nLab
Lie infinity-groupoid

Idea

A Lie $\mathrm{\infty }$-groupoid is supposed to be an ∞-groupoid internal to a suitable category of generalized smooth spaces; see internal ∞-groupoid.

Following the general idea of space and quantity and generalized smooth spaces one may identify smooth $\mathrm{\infty }$-groupoids with smooth infinity-stacks.

But notice that the traditional notion called Lie groupoid is more restritive than a 1-coskeletal smooth ∞-stack.

The details usually depend on which aspect of higher Lie theory one wants to capture.

A systematic setup is proposed at ∞-Lie theory.