chain complex

1. Definition

Let \(\mathcal{A}\) be a pointed category

A chain complex is a sequence \((M_n, d_n)\) of \(M_n \in \mathrm{Ob}(\mathcal{A})\) and morphisms \(d_n: M_n \rightarrow M_{n-1}\) such that

\begin{align*} d_n \circ d_{n+1} = 0 \end{align*}