Theorem 29.5:

Suppose given a pair of chain maps $\phi:L\longrightarrow G$ and $G\longrightarrow K$, then the composite $\psi\circ\phi:L\longrightarrow K$ is a chain map and

$$H_n(\psi\circ \phi) = H_n(\psi)\circ H_n(\phi), \quad n = 0, 1, 2,\dots \eqno(29.15)$$

In other words for each $n$ we get a covariant functor $H_n$ from the category of chain complexes to the category AbGr.