2004/04/16 by Daniel C. Isaksen, Isaksen, Daniel C.
Mathematics · #18G55 #55N10 (Primary) #55P60 #55U35 (Secondary) #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:18G55 #msc:55N10 #msc:55P60 #msc:55U35
paper · pdf · doi:10.48550/arxiv.math/0404303
arxiv created 2004/04/16 · arxiv updated 2009/12/01
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.