Definition 56.13.1. Let $\mathcal{A}$ be an abelian category. Let $\mathcal{D}$ be a triangulated category. We say two exact functors of triangulated categories

$F, F' : D^ b(\mathcal{A}) \longrightarrow \mathcal{D}$

are siblings, or we say $F'$ is a sibling of $F$, if the following two conditions are satisfied

1. the functors $F \circ i$ and $F' \circ i$ are isomorphic where $i : \mathcal{A} \to D^ b(\mathcal{A})$ is the inclusion functor, and

2. $F(K) \cong F'(K)$ for any $K$ in $D^ b(\mathcal{A})$.

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