The Stacks project

Definition 13.40.9. Let $\mathcal{D}$ be a triangulated category. A right admissible subcategory of $\mathcal{D}$ is a strictly full triangulated subcategory satisfying the equivalent conditions of Lemma 13.40.7. A left admissible subcategory of $\mathcal{D}$ is a strictly full triangulated subcategory satisfying the equivalent conditions of Lemma 13.40.8. A two-sided admissible subcategory is one which is both right and left admissible.