Lemma 22.26.9. Let $\varphi : (A, \text{d}) \to (E, \text{d})$ be a homomorphism of differential graded algebras. Then $\varphi$ induces a functor of differential graded categories

$F : \text{Mod}^{dg}_{(E, \text{d})} \longrightarrow \text{Mod}^{dg}_{(A, \text{d})}$

of Example 22.26.8 inducing obvious restriction functors on the categories of differential graded modules and homotopy categories.

Proof. Omitted. $\square$

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