A triangulated category is a mathematical structure used in the field of category theory, particularly in homological algebra. It consists of a category equipped with a class of distinguished triangles, which generalize the concept of exact sequences. These triangles help to capture the relationships between objects and morphisms, allowing for the study of their properties in a coherent way. In a triangulated category, the distinguished triangles satisfy certain axioms that facilitate the manipulation of these triangles. This framework is useful for various applications, including the study of derived categories and stable homotopy theory, providing a powerful tool for understanding complex algebraic and topological structures.