Subobject

In category theory, a branch of mathematics, a subobject of an object ${\displaystyle A}$ in a category is a monomorphism into ${\displaystyle A}$, “up to isomorphism”. In various categories of mathematical structures, this coincides with the standard notion of a substructure of the given type of structure. For example, subobjects correspond to subsets in the category of sets, to subgroups in the category of groups, to subrings in the category of rings, etc.

The dual concept to a subobject is a quotient object. This generalizes concepts such as quotient sets, quotient groups, quotient rings, etc.