Lemma 22.37.2. Let R be a ring. Let (A, \text{d}) and (B, \text{d}) be differential graded algebras over R. Let N be a differential graded (A, B)-bimodule. Assume that
N defines a compact object of D(B, \text{d}),
if N' \in D(B, \text{d}) and \mathop{\mathrm{Hom}}\nolimits _{D(B, \text{d})}(N, N'[n]) = 0 for n \in \mathbf{Z}, then N' = 0, and
the map H^ k(A) \to \mathop{\mathrm{Hom}}\nolimits _{D(B, \text{d})}(N, N[k]) is an isomorphism for all k \in \mathbf{Z}.
Then
gives an R-linear equivalence of triangulated categories.
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