#
nLab

loop groupoid

# Contents

## Definition

For $G$ a group and $\mathbf{B}G$ its one-object delooping groupoid, the **loop groupoid** $\mathcal{L}\mathbf{B}G$ of $G$ is the free loop space object of $\mathbf{B}G$.

This is the groupoid whose objects are the elements of $G$, and whose morphisms are of the form

$g \stackrel{h}{\to} h^{-1} g h
\,.$

## Applications

This plays a role in Dijkgraaf-Witten theory.

Created on September 8, 2010 19:41:01
by

Urs Schreiber
(77.80.23.231)