Lemma 18.37.1. Let \mathcal{C} be a site. Let p be a point of \mathcal{C} or of its associated topos.
The functor p_* : \textit{Ab} \to \textit{Ab}(\mathcal{C}), A \mapsto p_*A is exact.
There is a functorial direct sum decomposition
p^{-1}p_*A = A \oplus I(A)for A \in \mathop{\mathrm{Ob}}\nolimits (\textit{Ab}).
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