14 research outputs found
A convenient category of locally preordered spaces
As a practical foundation for a homotopy theory of abstract spacetime, we
extend a category of certain compact partially ordered spaces to a convenient
category of locally preordered spaces. In particular, we show that our new
category is Cartesian closed and that the forgetful functor to the category of
compactly generated spaces creates all limits and colimits.Comment: 26 pages, 0 figures, partially presented at GETCO 2005; changes:
claim of Prop. 5.11 weakened to finite case and proof changed due to problems
with proof of Lemma 3.26, now removed; Eg. 2.7, statement before Lem. 2.11,
typos, and other minor problems corrected throughout; extensive rewording;
proof of Lem. 3.31, now 3.30, adde
Gorenstein homological algebra and universal coefficient theorems
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 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