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Abelian Category

An Abelian category is a mathematical framework that organizes objects and morphisms (structural relationships) with properties similar to those in linear algebra. It allows for well-behaved concepts of addition, kernels, cokernels, and exact sequences, facilitating the study of algebraic structures like modules and vector spaces. In essence, an Abelian category provides a setting where one can perform algebraic operations systematically, ensuring that concepts like subtraction and the formation of exact sequences are meaningful and consistent, enabling deeper analysis within algebra, topology, and related fields.