A triangulated category is a type of mathematical structure used in the field of category theory, particularly in homological algebra. It extends the concept of a category by introducing a distinguished class of sequences called triangles, which help to capture the relationships between objects and morphisms. These triangles allow mathematicians to study properties like exactness and cohomology in a more flexible way. In a triangulated category, certain axioms govern how these triangles behave, ensuring that they can be manipulated similarly to exact sequences in traditional algebra. This framework is useful in various areas, including derived categories and stable homotopy theory, providing a powerful tool for understanding complex mathematical phenomena.