Injective object

Summary

An injective object of a category is an object $I$ such that maps into $I$ extend along every monomorphism. In a category of modules, the injective objects are exactly the injective modules. Among abelian groups they are the divisible groups, such as $\Q$ and $\Q/\Z$. Injective objects are used to build injective resolutions, from which right derived functors such as sheaf cohomology are computed. The dual notion is the projective object.