Lemma 24.28.3. In Lemma 24.28.1 the functor D(\mathcal{B}, \text{d}) \to D(\mathcal{A}', \text{d}) is equal to \mathcal{M} \mapsto Lf^*\mathcal{M} \otimes _\mathcal {A}^\mathbf {L} \mathcal{N}.
Proof. Immediate from the fact that we can compute these functors by representing objects by good differential graded modules and because f^*\mathcal{P} is a good differential graded \mathcal{A}-module if \mathcal{P} is a good differential graded \mathcal{B}-module. \square
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