\begin{definition}[Definition:Homology of Chain Complex]
Let $\AA$ be an abelian category.
Let $C := \family {d_i : C_i \to C_{i - 1} }_{i \mathop \in \Z}$ be a chain complex in $\AA$.
The $j$-th '''homology (object)''' $\map {H_j} C$ of $C$ is defined as the cokernel of the canonical map $\Img {d_{i + 1} } \to \ker \paren {d_i}$.
{{ExtractTheorem|Extract the following into its own page, as it is a result.}}
The canonical map is induced by Homomorphisms Theorem for Categories with Zero Object since by definition $d_{j} \circ d_{j + 1} = 0$.
\end{definition}