nLab loop groupoid



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 \,.


This plays a role in Dijkgraaf-Witten theory.

Created on September 8, 2010 at 19:41:02. See the history of this page for a list of all contributions to it.