Lemma 18.4.3 (03A9)—The Stacks project

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Lemma 18.4.3. Let $\mathcal{C}$ be a category. Let $I$ be a set. For each $i \in I$ let $\mathcal{G}_ i$ be a presheaf of sets. Then

$\mathbf{Z}_{\coprod _ i \mathcal{G}_ i} = \bigoplus \nolimits _{i \in I} \mathbf{Z}_{\mathcal{G}_ i}$

in $\textit{PAb}(\mathcal{C})$ .

Proof. Omitted. $\square$

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