The Stacks project

Definition 13.6.1. Let $\mathcal{D}$ be a pre-triangulated category. We say a full pre-triangulated subcategory $\mathcal{D}'$ of $\mathcal{D}$ is saturated if whenever $X \oplus Y$ is isomorphic to an object of $\mathcal{D}'$ then both $X$ and $Y$ are isomorphic to objects of $\mathcal{D}'$.

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