# nLab cochain complex

A cochain complex $V^\bullet$ in an Ab-enriched category $C$ is nothing but a chain complex in $C$, but with the sign of the $\mathbb{Z}$-grading reversed.

This means that for a cochain complex $(V^\bullet,d)$ the differential (or coboundary) $d$ increases the degree

$d : V^{k} \to V^{k+1} \,.$

# Examples

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