Auslander--Reiten theory in extriangulated categories

Understand

The notion of an extriangulated category gives a unification of existing theories in exact or abelian categories and in triangulated categories.

• In this article, we develop Auslander--Reiten theory for extriangulated categories.
• This unifies Auslander--Reiten theories developed in exact categories and triangulated categories independently.
• We give two different sets of sufficient conditions on the extriangulated category so that existence of almost split extensions becomes equivalent to that of an Auslander--Reiten--Serre duality.