Definition 13.3.1. Let \mathcal{D} be an additive category. Let [1] : \mathcal{D} \to \mathcal{D}, E \mapsto E[1] be an additive functor which is an auto-equivalence of \mathcal{D}.
A triangle is a sextuple (X, Y, Z, f, g, h) where X, Y, Z \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{D}) and f : X \to Y, g : Y \to Z and h : Z \to X[1] are morphisms of \mathcal{D}.
A morphism of triangles (X, Y, Z, f, g, h) \to (X', Y', Z', f', g', h') is given by morphisms a : X \to X', b : Y \to Y' and c : Z \to Z' of \mathcal{D} such that b \circ f = f' \circ a, c \circ g = g' \circ b and a[1] \circ h = h' \circ c.
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