The Stacks project

Lemma 24.21.3. Let $(\mathcal{C}, \mathcal{O})$ be a ringed site. Let $\mathcal{A}$ be a sheaf of differential graded algebras on $(\mathcal{C}, \mathcal{O})$. The homotopy category $K(\textit{Mod}(\mathcal{A}, \text{d}))$ has direct sums and products.

Proof. Omitted. Hint: Just use the direct sums and products as in Lemma 24.13.2. This works because we saw that these functors commute with the forgetful functor to the category of graded $\mathcal{A}$-modules and because $\prod $ and $\bigoplus $ are exact functors on the category of families of abelian groups. $\square$

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