nLab
infinity-Lie group

Definition

An smooth $\mathrm{\infty }$-group is a group object in the cohesive (∞,1)-topos Smooth∞Grpd of smooth ∞-groupoids.

Examples

Lie groups

An ordinary Lie group is a 0-truncated $\mathrm{\infty }$-Lie group.

Lie 2-groups

A Lie 2-group is a 1-truncated $\mathrm{\infty }$-Lie group.

• string 2-group

Lie 6-groups

A Lie 6-group is a 5-truncated $\mathrm{\infty }$-Lie group.

• fivebrane 6-group.

Related concepts

• cohesive (∞,1)-topos

  • discrete ∞-groupoid

  • Euclidean-topological ∞-groupoid

  • smooth ∞-groupoid

  • synthetic differential ∞-groupoid

References

See smooth ∞-groupoid.