Classifying Space
Any crossed module
has a classifying space BM with the property that its homotopy groups are Coker d, in dimension 1, Ker d in dimension 2, and 0 above 2. It is possible to describe conveniently the homotopy classes of maps from a CW-complex to BM. This allows one to prove that (pointed, weak) homotopy 2-types are completely described by crossed modules.
Read more about this topic: Crossed Module
Famous quotes containing the word space:
“The secret ones around a stone
Their lips withdrawn in meet surprise
Lie still, being naught but bone
With naught but space within their eyes....”
—Allen Tate (1899–1979)