nLab
infinity-Lie group

Context

Cohesive \infty-Toposes

cohesive topos

cohesive (∞,1)-topos

cohesive homotopy type theory

Backround

Definition

Presentation over a site

Structures in a cohesive (,1)(\infty,1)-topos

structures in a cohesive (∞,1)-topos

Structures with infinitesimal cohesion

infinitesimal cohesion?

Models

Differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

\infty-Lie theory

∞-Lie theory

Background

Smooth structure

Higher groupoids

Lie theory

∞-Lie groupoids

∞-Lie algebroids

Formal Lie groupoids

Cohomology

Homotopy

Examples

\infty-Lie groupoids

\infty-Lie groups

\infty-Lie algebroids

\infty-Lie algebras

Contents

Definition

An smooth \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 \infty-Lie group.

Lie 2-groups

A Lie 2-group is a 1-truncated \infty-Lie group.

Lie 6-groups

A Lie 6-group is a 5-truncated \infty-Lie group.

References

See smooth ∞-groupoid.

Revised on January 21, 2011 17:37:42 by Urs Schreiber (89.204.153.76)