In category theory, a branch of mathematics, the concept of an injective cogenerator is drawn from examples such as Pontryagin duality.
More precisely: Assuming one has a category like that of abelian groups, one can in fact form direct sums of copies of G until the morphism is surjective; and one can form direct products of C until the morphism is injective.
As an example of a cogenerator in the same category, we have Q/Z, the rationals modulo the integers, which is a divisible abelian group.
The cogenerator Q/Z is useful in the study of modules over general rings.
The Tietze extension theorem can be used to show that an interval is an injective cogenerator in a category of topological spaces subject to separation axioms.