Rick Jardine

Cocycle categories give a simple, flexible way to describe morphisms in a homotopy category, provided that the underlying model structure is sufficiently well behaved. "Well behaved" model structures include simplicial sets, spectra, simplicial...

Suppose that H is an algebraic group which is defined over a field k, and let L be the algebraic closure of k. The canonical stalk for the etale topology on k induces a simplicial set map from the classifying space B(H-tors) of the groupoid of H...

A Galois descent theorem for n-types will be displayed and explained. This result is used, together with an appropriate version of the homotopy theory of pro objects, to give a descent criterion for diagrams of spaces which are defined on the etale...

Finite cubical complexes are abstract models for parallel processing systems. The vertices of a complex K are the states of the system, and the execution paths are morphisms of the corresponding path category P(K). The theory of path categories and...

We start with a general introduction to pro-objects in topological and geometric settings, with descriptions of well-known examples, including Postnikov towers, absolute Galois groups, and etale homotopy types. This is followed by a brief discussion...