## Morphism of distinguished triangles where one of the arrows is a quasi-isomorphism

Let R be any ring and let A→B→C→[1] and A′→B′→C′→[1] be distinguished triangles of complexes of R-modules. Let f:A→A′, g:B→B′ and h:C→C′ be morphism of complexes such that (f,g,h) is a morphism of distinguished triangles. I wonder whether the following statement is true: If f:A→A′ is a quasi-isomorphism, then there is a quasi-isomorphism cone(g)∼→cone(h). Clearly, … Read more