Injective module

Summary

An injective module is a module $E$ such that every linear map into $E$ from a submodule extends to the whole module. It is the dual notion of a projective module, with the arrows reversed. Every module embeds into an injective module, and the smallest such embedding is the injective hull. Injective modules are used to build injective resolutions, which compute derived functors such as Ext and local cohomology.