Consider two (distinct) octahedral diagrams i.e. diagrams mentioned in the octahedron axioms of triangulated categories. Is it true than one can extend to a morphism of such diagrams:

1. a morphism of one of the 'commutative faces' of the octahedron 2 a morphism of the pair of morphisms whose target is the upper vertex of the octahedron?

Both of these statements seem to be easy, yet I am affraid to miss something. Could I write (in a paper) that these facts are well-known? Is there any text where I look for various facts of this sort?