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:
“No being exists or can exist which is not related to space in some way. God is everywhere, created minds are somewhere, and body is in the space that it occupies; and whatever is neither everywhere nor anywhere does not exist. And hence it follows that space is an effect arising from the first existence of being, because when any being is postulated, space is postulated.”
—Isaac Newton (1642–1727)