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There is a similar question herehere. It is asked in the particular case of the derived category of abelian groups and a counterexample is given by Tyler Lawson.

There is also an answer of mine which allows one to produce such triangles more generally.

There is a similar question here. It is asked in the particular case of the derived category of abelian groups and a counterexample is given by Tyler Lawson.

There is also an answer of mine which allows one to produce such triangles more generally.

There is a similar question here. It is asked in the particular case of the derived category of abelian groups and a counterexample is given by Tyler Lawson.

There is also an answer of mine which allows one to produce such triangles more generally.

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Greg Stevenson
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There is a similar question here. It is asked in the particular case of the derived category of abelian groups and a counterexample is given by Tyler Lawson.

There is also an answer of mine which allows one to produce such triangles more generally.