A Derived Category is a concept in the field of category theory, which is a branch of mathematics. It provides a way to study complexes of objects and morphisms in a more flexible manner. Derived categories allow mathematicians to work with homological algebra, focusing on the relationships between objects rather than just their individual properties. In a derived category, objects are typically chain complexes, which are sequences of objects connected by morphisms. This framework helps in understanding cohomology and derived functors, making it easier to analyze and compute properties of algebraic structures. Derived categories are essential in areas like algebraic geometry and representation theory.