Yoneda extensions of abelian quotient categories
Ramin Ebrahimi

TL;DR
This paper studies the behavior of Ext functors under quotient categories of abelian categories, providing conditions for when natural maps between Ext groups are isomorphisms, with an application included.
Contribution
It characterizes when the natural maps between Ext groups in an abelian category and its quotient are invertible up to a certain degree, extending understanding of Yoneda extensions in quotient categories.
Findings
Conditions for invertibility of Ext maps in quotient categories
Extension of Yoneda extension theory to abelian quotients
Application demonstrating the main theoretical results
Abstract
Let be a essentially small abelian category and be a Serre subcategory of . Consider the quotient functor . For an object and a non-negative integer we investigate when the natural map is invertible for every and every . In the end we give an application of the main theorem.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra
