\begin{definition}[Definition:Morphism of Chain Complexes]
Let $\AA$ be an abelian category.
Let $\family {C_i, d_i}_{i \mathop \in \Z}$ and $\family {C_i', d_i'}_{i \mathop \in \Z}$ be chain complexes in $\AA$.
A '''morphism of chain complexes''' from $\family {C_i}_{i \mathop \in \Z}$ to $\family {D_i}_{i \mathop \in \Z}$ is a family of morphisms $\family {f_i: C_i \to C_i'}_{i \mathop \in \Z}$, such that:
:$\forall i \in \Z: f_{i-1} \circ d_i = d_i' \circ f_i$
\end{definition}