Yoneda extensions of abelian quotient categories.

Let A be a essentially small abelian category and C be a Serre subcategory of A. Consider the quotient functor q : A → A / C. For an object A ∈ A and a non-negative integer k we investigate when the natural map q X , A i : Ext A i (X , A) → Ext A / C i (q (X) , q (A)) is invertible for every X ∈ A and every i ∈ { 0 , 1 , ⋯ , k }. In the end we give an application of the main theorem. [ABSTRACT FROM AUTHOR]