Lemma 13.4.19 (014Y)—The Stacks project

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Part 1: Preliminaries
Chapter 13: Derived Categories
Section 13.4: Elementary results on triangulated categories
Lemma 13.4.19 (cite)

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Lemma 13.4.19. Let $\mathcal{D}, \mathcal{D}', \mathcal{D}''$ be pre-triangulated categories. Let $F : \mathcal{D} \to \mathcal{D}'$ and $F' : \mathcal{D}' \to \mathcal{D}''$ be exact functors. Then $F' \circ F$ is an exact functor.

Proof. Omitted. $\square$

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