Lemma 22.5.4. Let $(A, \text{d})$ be a differential graded algebra. The homotopy category $K(\text{Mod}_{(A, \text{d})})$ has direct sums and products.

**Proof.**
Omitted. Hint: Just use the direct sums and products as in Lemma 22.4.2. This works because we saw that these functors commute with the forgetful functor to the category of graded $A$-modules and because $\prod $ is an exact functor on the category of families of abelian groups.
$\square$

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