  We study abelian quotient categories A=T/J, where T is a triangulated
category and J is an ideal of T. Under the assumption that the quotient functor
is cohomological we show that it is representable and give an explicit
description of the functor. We give technical criteria for when a representable
functor is a quotient functor, and a criterion for when J gives rise to a
cluster-tilting subcategory of T. We show that the quotient functor preserves
the AR-structure. As an application we show that if T is a finite 2-Calabi-Yau
category, then with very few exceptions J is a cluster-tilting subcategory of
T.
