Recall the homology group $H_n = \frac{\texttt{ker } \partial(n)}{\texttt{im } \partial(n + 1)}$ with the property $\partial^2 = 0$. In homoglogical algebra, a chain complex is a family $\{C_n\}_{n \in \mathbb{Z}}$ is a family of $R$-modules.

# Chain complexes

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