The Stacks project

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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