# The Groove of Math

## Random Exercise #3: K(G,1) is a model for the classifying space BG via covering theory (NOT l.e.s. of a fibration)

I decided to write down this nice exercise since it is the kind of exercise which is readily solved with the right tools (i.e. l.e.s. of a fibration), but can become non-trivial if one doesn’t know them.

In particular, I want to prove that the Eilenberg MacLance space $K(G,1)$, for a discrete group $G$ is a model for the classifying space $BG$.