2008/08/31 by Beatriz Rodríguez González, Beatriz Rodriguez Gonzalez
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #math.AG #math.AT #math.CT #math.KT #msc:14F35 #msc:18D99 #msc:18G30
paper · pdf · doi:10.1016/j.jpaa.2011.10.003
Final version. To appear in the J. Pure Appl. Algebra
arxiv created 2011/10/11 · arxiv updated 2011/10/12 · openalex publication_date 2011/10/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
In this paper we study the question of how to transfer homotopic structure from the category sD of simplicial objects in a fixed category D to D. To this end we use a sort of homotopy colimit s : sD --> D, which we call simple functor. For instance, the Bousfield-Kan homotopy colimit in a Quillen simplicial model category is an example of simple functor. As a remarkable example outside the setting of Quillen models we include Deligne simple of mixed Hodge complexes. We prove here that the simple functor induces an equivalence on the corresponding localized categories. We also describe a natural structure of Brown category of cofibrant objects on sD. We use these facts to produce cofiber sequences on the localized category of D by E, which give rise to a natural Verdier triangulated structure in the stable case.