Nonisomorphic Verdier octahedra on the same base

We show by an example that in a Verdier triangulated category, there may exist two mutually nonisomorphic Verdier octahedra containing the same commutative triangle.

💡 Research Summary

The paper investigates a subtle but important point in the theory of Verdier triangulated categories: the non‑uniqueness of octahedra that extend a given Verdier triangle. In a Verdier triangulated category, a Verdier triangle consists of three composable morphisms (X \xrightarrow{f} Y \xrightarrow{g} Z) together with a distinguished triangle (X \xrightarrow{f} Y \xrightarrow{g} Z \xrightarrow{h} X