Nonisomorphic Verdier octahedra on the same base

TL;DR

This paper demonstrates that in a Verdier triangulated category, two nonisomorphic Verdier octahedra can share the same base triangle, highlighting structural differences within the category.

Contribution

The paper provides a specific example showing the existence of nonisomorphic Verdier octahedra with identical bases, revealing new insights into the structure of Verdier triangulated categories.

Findings

Existence of nonisomorphic Verdier octahedra with the same base

Counterexample to potential uniqueness assumptions

Structural complexity in Verdier triangulated categories

Abstract

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