The Stacks project

Definition 13.6.5. Let $\mathcal{D}$ be a (pre-)triangulated category.

  1. Let $F : \mathcal{D} \to \mathcal{D}'$ be an exact functor. The kernel of $F$ is the strictly full saturated (pre-)triangulated subcategory described in Lemma 13.6.2.

  2. Let $H : \mathcal{D} \to \mathcal{A}$ be a homological functor. The kernel of $H$ is the strictly full saturated (pre-)triangulated subcategory described in Lemma 13.6.3.

These are sometimes denoted $\mathop{\mathrm{Ker}}(F)$ or $\mathop{\mathrm{Ker}}(H)$.

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  • 2 comment(s) on Section 13.6: Quotients of triangulated categories

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View Definition 13.6.5 as pdf