In mathematics, particularly in the field of algebraic geometry and homological algebra, a **derived category** is a concept that allows one to work with complexes of objects (such as sheaves, abelian groups, or modules) in a way that takes into account their morphisms up to homotopy. Derived categories provide a framework for studying how complex objects relate to one another and for performing calculations in a more flexible manner than is possible in the traditional context of abelian categories.
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