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 is an element of A and a non-negative integer k we investigate when the natural map qiX,A : ExtiA(X, A)-+ ExtiA/C(q(X), q(A)) is invertible for every X is an element of A and every i is an element of {0, 1, middot middot middot, k}. In the end we give an application of the main theorem.(c) 2022 Elsevier Inc. All rights reserved.

Automated summary

This article investigates the invertibility condition of the natural map qiX,A: ExtiA(X, A) to ExtiA/C(q(X), q(A)) for every object X and A, and every i in {0, 1, ..., k} in a essentially small abelian category A with a given Serre subcategory C. An application of the main theorem is also provided.