In mathematics, particularly in category theory, a morphism is a structure-preserving map between two objects. Morphisms can represent various types of relationships, such as functions between sets or linear transformations between vector spaces. They help to illustrate how different mathematical structures relate to one another. Morphisms are essential for understanding the concept of categories, which consist of objects and morphisms between them. Each morphism has a source object and a target object, and they can be composed if the target of one morphism matches the source of another. This composition property is fundamental in defining the structure of categories and their applications in various fields of mathematics.