Abstract
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 qX,Ai:ExtAi(X,A)→ExtA/Ci(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.
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