The Stacks project

Lemma 22.26.7. Let $F : \mathcal{B} \to \mathcal{B}'$ be an additive functor between additive categories. Then $F$ induces a functor of differential graded categories

\[ F : \text{Comp}^{dg}(\mathcal{B}) \to \text{Comp}^{dg}(\mathcal{B}') \]

of Example 22.26.6 inducing the usual functors on the category of complexes and the homotopy categories.

Proof. Omitted. $\square$

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