# Contents

## Definition

For $G$ a group and $BG$ its one-object delooping groupoid, the loop groupoid $ℒBG$ of $G$ is the free loop space object of $BG$.

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

$g\stackrel{h}{\to }{h}^{-1}gh\phantom{\rule{thinmathspace}{0ex}}.$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)