The Stacks project

Lemma 13.35.4. Let $\mathcal{T}$ be a triangulated category. Given a full subcategory $\mathcal{A}$ for $n \geq 1$ the subcategory

\[ \mathcal{C}_ n = smd(add(\mathcal{A})^{\star n}) = smd(add(\mathcal{A}) \star \ldots \star add(\mathcal{A})) \]

defined above is a strictly full subcategory of $\mathcal{T}$ closed under direct sums and direct summands and $\mathcal{C}_{n + m} = smd(\mathcal{C}_ n \star \mathcal{C}_ m)$ for all $n, m \geq 1$.

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