= Čech-de Rham double complex
{c}
{title2=$D_{\mathrm{tot}}=\delta+(-1)^p d$}
On a good cover, combine Čech degree $p$ and differential-form degree $q$ in the double complex of forms on intersections. The Čech differential and <exterior derivative> commute, so the total differential $\delta+(-1)^p d$ squares to zero. A partition of unity and the <Poincare lemma> identify its cohomology with both constant-sheaf and <de Rham cohomology>. The sign convention makes <Čech-de Rham curvature descent> explicit.
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