Lemma 12.24.3. Let $\mathcal{A}$ be an abelian category. Suppose $I_\omega$, $\omega \in \Omega$ is a set of injective objects of $\mathcal{A}$. If $\prod _{\omega \in \Omega } I_\omega$ exists then it is injective.

Proof. Omitted. $\square$

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