Lemma 13.25.1 (05TN)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 13: Derived Categories
Section 13.25: Right derived functors via resolution functors
Lemma 13.25.1 (cite)

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Lemma 13.25.1. Let $\mathcal{A}$ be an abelian category with enough injectives Let $F : \mathcal{A} \to \mathcal{B}$ be an additive functor into an abelian category. Let $(i, j)$ be a resolution functor, see Definition 13.23.2. The right derived functor $RF$ of $F$ fits into the following $2$ -commutative diagram

$\xymatrix{ D^{+}(\mathcal{A}) \ar[rd]_{RF} \ar[rr]^{j'} & & K^{+}(\mathcal{I}) \ar[ld]^ F \\ & D^{+}(\mathcal{B}) }$

where $j'$ is the functor from Lemma 13.23.6.

Proof. By Lemma 13.20.1 we have $RF(K^\bullet ) = F(j(K^\bullet ))$ . $\square$

Comments (1)

Comment #723 by Kestutis Cesnavicius on June 21, 2014 at 20:34

Right before this lemma a closing parenthesis is missing.

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