  We prove that some subquotient categories of exact categories are abelian.
This generalizes a result by Koenig-Zhu in the case of (algebraic) triangulated
categories. As a particular case, if an exact category B with enough
projectives and injectives has a cluster tilting subcategory M, then B/M is
abelian. More precisely, it is equivalent to the category of finitely presented
modules over the stable category of M.

Representation Theory;Category Theory