Lemma 22.9.1 (09KB)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 22: Differential Graded Algebra
Section 22.9: Cones and distinguished triangles
Lemma 22.9.1 (cite)

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Lemma 22.9.1. Let $(A, \text{d})$ be a differential graded algebra. Let $f : K \to L$ be a homomorphism of differential graded modules. The triangle $(L, C(f), K[1], i, p, f[1])$ is the triangle associated to the admissible short exact sequence

$0 \to L \to C(f) \to K[1] \to 0$

coming from the definition of the cone of $f$ .

Proof. Immediate from the definitions. $\square$

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