A stable category is a mathematical structure used in the field of category theory, particularly in the study of homological algebra. It provides a framework to analyze objects and morphisms in a way that allows for the definition of concepts like exact sequences and derived functors. Stable categories are characterized by the presence of a "shift" functor, which helps in understanding the relationships between objects. In a stable category, morphisms can be classified as "stable" under certain conditions, meaning that they behave consistently when shifted. This concept is particularly useful in the study of triangulated categories and derived categories, where stability helps in understanding the underlying algebraic structures.