**2**

votes

**2**answers

837 views

### Splitting in triangulated categories

Using the axioms for a triangulated category, is it possible to prove the following:
$A\stackrel{0}{\to}B\to A\oplus B\to$ is a distinguished triangle.
From the first axiom, the map ...

**7**

votes

**3**answers

689 views

### If a colimit of distinguished triangles exists, is it also a distinguished triangle?

Consider the following situation in some triangulated category: We are given a collection of distinguished triangles $A_n \to B_n \to C_n \to A_n[1]$ indexed by the natural numbers, together with maps ...