Right derived functors are a way to extend the notion of a functor to measure how much the functor fails to be exact when applied to chain complexes. They provide crucial insights into the homological properties of objects in categories, especially in the context of abelian categories. This concept is foundational in homological algebra, allowing mathematicians to study the behavior of functors like Hom and Tensor, and to understand their relationships with projective and injective modules.
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