An injective resolution of an object 
in an Abelian category
is an exact sequence
in which each 
is an injective object. Such a resolution exists
for every object when the Abelian
category has enough injectives, meaning that every object
admits a monomorphism into an injective
object (Stacks Project n.d., Definition 13.18.1 and Lemma 13.18.3). Applying
an additive functor to the cochain
complex 
and taking cohomology computes its right derived functors
when these resolutions are available.
See also
Derived Functor,
Exact Sequence,
Injective Object,
Projective
Resolution
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References
Stacks Project. "Injective Resolutions." Definition 13.18.1 and Lemma 13.18.3, Tag 013G. https://stacks.math.columbia.edu/tag/013G.Stacks
Project. "Right Derived Functors and Injective Resolutions." §13.20,
Tag 0156. https://stacks.math.columbia.edu/tag/0156.
Cite this as:
Weisstein, Eric W. "Injective Resolution."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/InjectiveResolution.html
Subject classifications
