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Paper   IPM / M / 8906
School of Mathematics
  Title:   Gorenstein cohomology in Abelian categories
  Author(s):  T. Sharif (Joint with S. Sather-Wagstaff and D. White)
  Status:   Published
  Journal: J. Math. Kyoto Univ.
  Vol.:  48
  Year:  2008
  Pages:   571-596
  Supported by:  IPM
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.

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