# How is the delooping of a groupoid constructed explicitly?

Let $G$ be a group, nlab's "delooping" page says that $G$ can be considered as a discrete groupoid in the $(\infty,1)$-topos $\infty$Grpd of $\infty$-grupoids, the delooping of $BG$ is then the groupoid with a single object $\bullet$ and morphisms given by $hom_{BG}(\bullet, \bullet)$. I'm interested to see how $BV$ is constructed for a general groupoid $V$, I'd read about homotopy limits and kind of had the notion of what they are, I went to the "homotopy pullback" section (http://ncatlab.org/nlab/show/homotopy+limit#HomotopyPullbacks) on nlab's "homotopy limit" page to see how $BG$ is constructed for an ordinary group $G$, I was sort of following what they were saying but got stuck with this:

1 - Didn't know what a "generalized universal bundle" is, and why is it weakly equivalent to $pt$?

2 - They say that the homotopy limit in question is directly seen to be Disc(Obj(EG)) = Disc(Obj(G//G)) = Disc(G), what is Disc supposed to mean here?

Anyone know?

• I think Disc is supposed to be the collection of discrete objects.
– user122283
Aug 28, 2015 at 2:07