Homotopy group with coefficients

In topology, a branch of mathematics, for $i \ge 2$, 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 $(G, i)$ to X, and is denoted by $\pi_i(X; G)$.^[1] For $i \ge 3$, $\pi_i(X; G)$ is a group. Note $\pi_i(X; \mathbb{Z})$ are the usual homotopy groups of X.

References

1. Weibel 2013, Ch. IV. Definition 2.1

• C. Weibel "The K-book: An introduction to algebraic K-theory"