Injective Resolution

An exact chain complex I• of injective objects together with a monomorphism M → I0 embedding the given object or module M so that M → I• is a quasi-isomorphism in positive degrees; used to compute right-derived functors by applying a left-exact functor to I• and taking homology.

An injective resolution of an object M in an abelian category is an exact complex 0→M→I^0→I^1→… with each I^i injective; such a coresolution is used to compute right-derived functors, e.g., Ext^i(−,M) or the derived functors R^iΓ for a left-exact functor Γ.