2007/06/26 by Sather-Wagstaff, Sean, Sharif, Tirdad, White, Diana
#13D05 #13D07 #18G15 #18G20 #18G25 #Commutative Algebra (math.AC) #FOS: Mathematics #K-Theory and Homology (math.KT) #Primary 18G10 #Secondary 13D02
paper · doi:10.48550/arxiv.0706.3739
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 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.