 Eilenberg–MacLane space

For an abelian group $A$, an Eilenberg–MacLane space $K(A,n)$ has ${\pi }_n\cong A$ and all other homotopy groups trivial. In the simplicial model it is $K(A[n])$, where $A[n]$ is the chain complex concentrated in degree $n$.

An Eilenberg-MacLane space is a fundamental concept in algebraic topology, named after mathematicians Samuel Eilenberg and Saunders Mac Lane. It is used to study topological properties related to cohomology theories and homotopy theory.