2013/04/22 by David Blanc, Blanc, David, Debasis Sen +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:55P20 #msc:55P48 #msc:55P60 #msc:55U35
paper · pdf · doi:10.48550/arxiv.1304.5928
38 pages, revised version
arxiv created 2014/01/14 · arxiv updated 2014/01/15
We study the questions of how to recognize when a simplicial set X is of the form X=map(Y,A) for a given space A, and how to recover Y from X, if so. A full answer is provided when A=K(R,n), for R=\mathbbFp or ℚ, in terms of a mapping algebra structure on X (defined in terms of product-preserving simplicial functors out of a certain simplicially-enriched sketch). In addition, when A is a suitable infinite loop space for a suitable connective ring spectrum, we can recover Y from map(Y,A) given such a mapping algebra structure. Most importantly, our methods provide a new way of looking at the classical Bousfield-Kan R-completion.