Theorem 29.4:

A chain map $\phi:G\longrightarrow K$ induces for each $n = 0, 1, 2, \dots,$ a group homomorphism $H_n(\phi):H_n(G)\longrightarrow H_n(K)$ given by

$$\overline{x} \;\mapsto\; \overline{\phi_n(x)}.$$