Author: Daniel C. Isaksen
Author's e-mail address: isaksen@math.wayne.edu
Author's mailing address: Department of Mathematics \\ 
Wayne State University \\ Detroit, MI 48202
Included ps or eps files: None
AMS classification number: 55P60, 55N10 (Primary); 18G55, 55U35 (Secondary)
Abstract: 

For every ring R, we present a pair of model structures on the category 
of pro-spaces.  In the first, the weak equivalences are detected by 
cohomology with coefficients in R.  In the second, the weak equivalences 
are detected by cohomology with coefficients in all R-modules (or 
equivalently by pro-homology with coefficients in R).  In the second 
model structure, fibrant replacement is essentially just the 
Bousfield-Kan R-tower.  When R = Z/p, the first homotopy category 
is equivalent to a homotopy theory defined by Morel but has some 
convenient categorical advantages.