Čech-de Rham double complex ($D_{\mathrm{tot}}=\delta +(-1{)}^{p}d$)

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.