An injective object 
in an Abelian category is an object
with the following extension property: for every monomorphism 
and every morphism 
, there is a morphism 
with 
. Equivalently, the hom functor 
is an exact
functor.
An Abelian category has enough injectives if every object admits a monomorphism into an injective object (The Stacks Project Authors 2026). In the category of modules over a unit ring, the injective objects are precisely the injective modules. Enough injectives is one of the hypotheses for the Grothendieck spectral sequence.
