nLab
loop groupoid

Contents

Definition

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

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

ghh 1gh. 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)