Lemma 22.22.3. Let $(A, \text{d})$ be a differential graded algebra. Let $M$ and $N$ be differential graded $A$-modules.

Let $P \to M$ be a P-resolution as in Lemma 22.20.4. Then

\[ \mathop{\mathrm{Hom}}\nolimits _{D(A, \text{d})}(M, N) = \mathop{\mathrm{Hom}}\nolimits _{K(\text{Mod}_{(A, \text{d})})}(P, N) \]Let $N \to I$ be an I-resolution as in Lemma 22.21.4. Then

\[ \mathop{\mathrm{Hom}}\nolimits _{D(A, \text{d})}(M, N) = \mathop{\mathrm{Hom}}\nolimits _{K(\text{Mod}_{(A, \text{d})})}(M, I) \]

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