Distinguished triangle
A triangle selected to play the role of an exact sequence in a shifted additive category.
A distinguished triangle is a triangle
belonging to the specified class of a pretriangulated category (or a triangulated category). The class, together with the category and shift, must satisfy the complete axioms given there.
Mapping-cone interpretation
It abstracts the mapping-cone sequence of a chain map and plays the role that a short exact sequence plays in an abelian category.
The class is closed under isomorphism and rotation, and every morphism must occur as the first map of some distinguished triangle. The precise coherence requirements distinguish a pretriangulated category from an arbitrary shifted preadditive category.