Subobject

In category theory, a branch of mathematics, a subobject is, roughly speaking, an object which sits inside another object in the same category. The notion is a generalization of the older concepts of subset from set theory and subgroup from group theory. Since the actual structure of objects is immaterial in category theory, the definition of subobject relies on a morphism which describes how one object sits inside another, rather than relying on the use of elements.