Lemma 19.13.2. A Grothendieck abelian category has Ab3*.

**Proof.**
Let $M_ i$, $i \in I$ be a family of objects of $\mathcal{A}$ indexed by a set $I$. The functor $F = \prod _{i \in I} h_{M_ i}$ commutes with colimits. Hence Lemma 19.13.1 applies.
$\square$

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