107 research outputs found
Enriched model categories and presheaf categories
We collect in one place a variety of known and folklore results in enriched
model category theory and add a few new twists. The central theme is a general
procedure for constructing a Quillen adjunction, often a Quillen equivalence,
between a given V-model category and a category of enriched presheaves in V,
where V is any good enriching category. For example, we rederive the result of
Schwede and Shipley that reasonable stable model categories are Quillen
equivalent to presheaf categories of spectra (alias categories of module
spectra) under more general hypotheses. The technical improvements and
modifications of general model categorical results given here are applied to
equivariant contexts in a pair of sequels, where we indicate various directions
of application.Comment: 45 pages. v4. A number of relatively small changes and updates from
the previous version, intended to address the most recent referee's report.
The most significant change is the addition of section 4.5, which discusses
Muro's work on arranging for a cofibrant uni
Stiffness of finite free resolutions and the Canonical Element Conjecture
Over a noetherian local ring certain minimal finite free resolutions possess
a property which we call stiffness. This calls to mind the Buchsbaum-Eisenbud
criterion for exactness. Yet we only prove stiffness over equicharacteristic
rings. However, Hochster's Canonical Element Conjecture is shown to be true for
every ring with a fixed prime residual characteristic, precisely when every
resolution over each Gorenstein ring of this type is stiff.Comment: 11 page
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