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We begin by showing that in a triangulated category, specifying a projective class is equivalent to specifying an ideal I of morphisms with certain properties, and that if I has these properties,… (More)

Freyd's generating hypothesis, interpreted in the stable module category of a finite p-group G, is the statement that a map between finite-dimensional kG-modules factors through a projective if the… (More)

We propose a structure called a causal site to use as a setting for quantum geometry, replacing the underlying point set. The structure has an interesting categorical form, and a natural “tangent… (More)

An important example of a model category is the category of unbounded chain complexes of R-modules, which has as its homotopy category the derived category of the ring R. This example shows that… (More)

Using numerical calculations, we compare three versions of the Barrett–Crane model of four-dimensional Riemannian quantum gravity. In the version with face and edge amplitudes as described by De… (More)

We numerically study Barrett–Crane models of Riemannian quantum gravity. We have extended the existing numerical techniques to handle q-deformed models and arbitrary spacetime triangulations. We… (More)

The Riemannian 10j symbols are spin networks that assign an amplitude to each 4-simplex in the Barrett-Crane model of Riemannian quantum gravity. This amplitude is a function of the areas of the 10… (More)

A ghost over a finite p-group G is a map between modular representations of G which is invisible in Tate cohomology. Motivated by the failure of the generating hypothesis—the statement that ghosts… (More)

Cofiltered diagrams of spectra, also called pro-spectra, have arisen in diverse areas, and to date have been treated in an ad hoc manner. The purpose of this paper is to systematically develop a… (More)

Smooth manifolds are central objects in mathematics. However, the category of smooth manifolds is not closed under many useful operations. Since the 1970’s, mathematicians have been trying to… (More)