nLab
formal cohesive infinity-groupoid

Context

\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

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 \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 \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 \infty-groupoid is the terminal object, it is the delooping of a formal ∞-group .

Created on April 13, 2011 21:56:53 by Urs Schreiber (82.113.99.35)