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 a specified class that is required to satisfy the triangle axioms. 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.