2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/132442We investigate relative cohomology functors on subcategories of abelian categories via Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that certain comparison maps between these functors are isomorphisms and introduce a notion of perfection for this context. Our main theorem is a balance result for relative cohomology that simultaneously recovers theorems of Holm and the current authors as special cases.22 pagesK-Theory and HomologyCommutative AlgebraPrimary 18G10, 18G15, 18G20, 18G25; Secondary 13D02, 13D05, 13D07text