Čech cohomology
= Čech cohomology
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{title2=$\check H^p(\mathcal U,\mathcal F)$}
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For an open cover $\mathcal U=(U_i)$, the Čech cochain group is
$$
\check C^p(\mathcal U,\mathcal F)=\prod_{i_0<\cdots<i_p}\mathcal F(U_{i_0}\cap\cdots\cap U_{i_p}),
$$
with the alternating sum of restrictions as differential. Its cohomology is the Čech cohomology of $\mathcal F$ with respect to $\mathcal U$.