What is Homotopy group with coefficients?

In topology, a branch of mathematics, for i ≥ 2 {\displaystyle i\geq 2} , the i-th homotopy group with coefficients in an abelian group G of a based space X is the pointed set of homotopy classes of based maps from the Moore space of type {\displaystyle } to X, and is denoted by π i {\displaystyle \pi _{i}}. For i ≥ 3 {\displaystyle i\geq 3} , π i {\displaystyle \pi _{i}} is a group. The groups π i {\displaystyle \pi _{i}} are the usual homotopy groups of X.