Let R be a noetherian ring, and denote the full subcategories of R-modules L such that Exti(E,L)=0 for all injective R-modules E for 1⋚i⋚n and O⋚i⋚n by Cn, and C′nrespectively. Then LεCn, if and only if every injective resolution of L is an injective resolvent of the nth cosyzygy. In this case, L is not injective if and only if its injective dimension is greater than n. If LεC′nand idN⋚n. then Hom(N,L)=0 for all R-modules N. As an application, let Knbe the nth syzygy of an injective resolvent of the nth cosyzygy of an R-module N, then there exists a homomorphism φ:N → K such that ((φ,iN), Kn• E(N)) and (φ,Kn) are preenvelopes of N for Csand C′srespectively, for s≥n. If the global dimension of R is at most 2, then C′1is reflective in the category of R-modules.