Lemma 13.4.9. Let $\mathcal{D}$ be a pre-triangulated category. Let $f : X \to Y$ be a morphism of $\mathcal{D}$. The following are equivalent

$f$ is an isomorphism,

$(X, Y, 0, f, 0, 0)$ is a distinguished triangle, and

for any distinguished triangle $(X, Y, Z, f, g, h)$ we have $Z = 0$.

## Comments (1)

Comment #379 by Fan on

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