Gorenstein homological algebra and universal coefficient theorems

Abstract

We study criteria for a ring -- or more generally, for a small category -- to be Gorenstein and for a module over it to be of finite projective dimension. The goal is to unify the universal coefficient theorems found in the literature and to develop a machinery for proving new ones. Among the universal coefficient theorems covered by our methods we find, besides all the classic examples, several exotic examples arising from the KK-theory of C*-algebras and also Neeman'\''s Brown-Adams representability theorem for compactly generated categories.