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

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.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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