Lemma 56.4.5. With $A$, $B$, $F$, and $F'$ as in Lemma 56.4.1. Assume $A$ is a coherent ring (Algebra, Definition 10.90.1). If $F$ is left exact, then $F'$ is left exact.

**Proof.**
Special case of Lemma 56.2.4.
$\square$

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