Derived functor

In mathematics, particularly in the field of category theory and homological algebra, derived functors are a way of extending the notion of a functor by capturing information about how it fails to be exact. ### Background In general, a functor is a map between categories that preserves the structure of those categories. An exact functor is one that preserves exact sequences, which are sequences of objects and morphisms that exhibit a certain algebraic structure, particularly in the context of abelian categories.