The Stacks project

Lemma 35.4.10. For a ring $R$, the functor $C : \text{Mod}_ R \to \text{Mod}_ R$ is exact and reflects injections and surjections.

Proof. Exactness is More on Algebra, Lemma 15.55.6 and the other properties follow from this, see Remark 35.4.4. $\square$

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