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
Comments (0)