\begin{definition}[Definition:Exact Chain Complex]
Let $\AA$ be an abelian category.
Let $\family {d_i : C_i \to C_{i - 1} }_{i \mathop \in \Z}$ be a chain complex in $\AA$.
Then $\family {d_i : C_i \to C_{i - 1} }_{i \mathop \in \Z}$ is '''exact''' {{iff}} it is exact at $C_i$ for all $i \mathop \in \Z$.
\end{definition}