Homotopy group with coefficients

In algebraic topology, homotopy groups are algebraic invariants that classify topological spaces up to homotopy equivalence. Typically, the most commonly discussed homotopy groups are the homotopy groups of a space \( X \), denoted \( \pi_n(X) \), which for a given integer \( n \) represent the \( n \)-th homotopy group of \( X \).