  We study Auslander-Reiten theory in proper abelian subcategories of
triangulated categories with a Serre functor. To initiate this, we use
approximations of a Serre functor to construct Nakayama functors, which in turn
allow for the construction of Auslander-Reiten translates and the existence of
Auslander-Reiten sequences in suitable proper abelian subcategories. As an
application, we recover the existence of Auslander-Reiten sequences in the
category of finite dimensional modules over a finite dimensional algebra.
