Mutation pairs and quotient categories of Abelian categories

The notion of ?-mutation pairs of subcategories in an abelian category is defined in this article. When (?,?) is a ?-mutation pair in an abelian category ?, the quotient category ?/? carries naturally a triangulated structure. Moreover, our result generalize the construction of the quotient triangulated category by Happel [10, Theorem 2.6]. Finally, we find a one-to-one correspondence between cotorsion pairs in ? and cotorsion pairs in the quotient category ?/?, and study homological finiteness of subcategories in a mutation pair.