The Stacks project

Remark 22.37.3. In Lemma 22.37.2 we can replace condition (2) by the condition that $N$ is a classical generator for $D_{compact}(B, d)$, see Derived Categories, Proposition 13.37.6. Moreover, if we knew that $R\mathop{\mathrm{Hom}}\nolimits (N, B)$ is a compact object of $D(A, \text{d})$, then it suffices to check that $N$ is a weak generator for $D_{compact}(B, \text{d})$. We omit the proof; we will add it here if we ever need it in the Stacks project.