Lemma 24.23.3 (0FSD)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 24: Differential Graded Sheaves
Section 24.23: Flat resolutions
Lemma 24.23.3 (cite)

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Lemma 24.23.3. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\mathcal{A}$ be a sheaf of differential graded algebras on $(\mathcal{C}, \mathcal{O})$ . An arbitrary direct sum of good differential graded $\mathcal{A}$ -modules is good. A filtered colimit of good differential graded $\mathcal{A}$ -modules is good.

Proof. Omitted. Hint: direct sums and filtered colimits commute with tensor products and with pullbacks. $\square$

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