Definition 57.10.1. 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
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
F(K) \cong F'(K) for any K in D^ b(\mathcal{A}).
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