Lemma 12.10.4 (02MQ)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 12: Homological Algebra
Section 12.10: Serre subcategories
Lemma 12.10.4 (cite)

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Lemma 12.10.4. Let $\mathcal{A}$ , $\mathcal{B}$ be abelian categories. Let $F : \mathcal{A} \to \mathcal{B}$ be an exact functor. Then the full subcategory of objects $C$ of $\mathcal{A}$ such that $F(C) = 0$ forms a Serre subcategory of $\mathcal{A}$ .

Proof. Omitted. $\square$

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