Remark 13.35.5. Let F : \mathcal{T} \to \mathcal{T}' be an exact functor of triangulated categories. Given a full subcategory \mathcal{A} of \mathcal{T} we denote F(\mathcal{A}) the full subcategory of \mathcal{T}' whose objects consists of all objects F(A) with A \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{A}). We have
F(\mathcal{A}[a, b]) = F(\mathcal{A})[a, b]
F(smd(\mathcal{A})) \subset smd(F(\mathcal{A})),
F(add(\mathcal{A})) \subset add(F(\mathcal{A})),
F(\mathcal{A} \star \mathcal{B}) \subset F(\mathcal{A}) \star F(\mathcal{B}),
F(\mathcal{A}^{\star n}) \subset F(\mathcal{A})^{\star n}.
We omit the trivial verifications.
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