Čech differential
= Čech differential
{c}
{title2=$\delta:\check C^p\to\check C^{p+1}$}
The Čech differential sends a cochain on $(p+1)$-fold intersections to the alternating sum of its restrictions to $(p+2)$-fold intersections. Each pair of omitted indices occurs twice with opposite signs in the composite, so $\delta^2=0$. It defines the <Čech cohomology> of the cover.