= Exact triangle in a derived category
= Exact triangle
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= Distinguished triangle
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An exact, or distinguished, triangle is one isomorphic to $E\xrightarrow{f}F\to\operatorname{Cone}(f)\to E[1]$. For a degreewise short exact sequence $0\to E\to F\to G\to0$, the map $\operatorname{Cone}(f)\to G$ taking $(v,e)$ to the image of $v$ is a <quasi-isomorphism>: its kernel is the contractible cone of the identity on $E$. Consequently the short exact sequence defines such a triangle.
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