Lemma 22.21.1 (09KR)—The Stacks project

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Part 1: Preliminaries
Chapter 22: Differential Graded Algebra
Section 22.21: I-resolutions
Lemma 22.21.1 (cite)

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Lemma 22.21.1. Let $(A, \text{d})$ be a differential graded algebra. Let $I$ be a differential graded $A$-module. If $F_\bullet $ is a filtration as in property (I), then we obtain an admissible short exact sequence

\[ 0 \to I \to \prod \nolimits I/F_ iI \to \prod \nolimits I/F_ iI \to 0 \]

of differential graded $A$-modules.

Proof. Omitted. Hint: This is dual to Lemma 22.20.1. $\square$

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