2011/04/04 by Beatriz Rodríguez González, Beatriz Rodriguez Gonzalez, Gonzalez, Beatriz Rodriguez
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AG #math.AT #math.CT #math.KT
paper · pdf · doi:10.48550/arxiv.1104.0646
34 pages; some results generalized and the presentation is improved
openalex publication_date 2011/04/04 · arxiv created 2012/02/16 · arxiv updated 2012/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove that for any model category, the Bousfield-Kan construction of the homotopy colimit is the absolute left derived functor of the colimit. This is achieved by showing that the Bousfield-Kan homotopy colimit is moreover a realizable homotopy colimit, defined by means of a suitable 2-category of relative categories. In addition, in the case of exact coproducts, we characterize the realizable homotopy colimits that satisfy a cofinality property as those given by a formula following the pattern of Bousfield-Kan construction: they are the composition of a "geometric realization" with the simplicial replacement.