Given two objects in a (locally small) category, say and , there is a set , called a hom-set, whose elements are morphisms from to . Given a morphism in this hom-set, we write to indicate that it goes from to .
More generally, a morphism is what goes between objects in any n-category.
The most familiar example is the category Set, where the objects are sets and the morphisms are functions. Here if and are sets, a morphism is a function from to .