\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
We 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 perfectness for this context. Our main theorem
is a balance result for relative cohomology that simultaneously
recovers theorems of Holm and current authors as special cases.
\end{document}