Definition 59.18.1. Let $\mathcal{C}$ be a category. Let $\mathcal{U} = \{ U_ i \to U\} _{i \in I}$ be a family of morphisms of $\mathcal{C}$ with fixed target. Assume that all the fibre products $U_{i_0} \times _ U \ldots \times _ U U_{i_ p}$ exists in $\mathcal{C}$. Let $\mathcal{F} \in \textit{PAb}(\mathcal{C})$ be an abelian presheaf. We define the *Čech complex* $\check{\mathcal{C}}^\bullet (\mathcal{U}, \mathcal{F})$ by

where the first term is in degree 0 and the maps are the usual ones. The *Čech cohomology groups* are defined by

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Comment #8255 by Haohao Liu on

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