2011/03/23 by A.R. Garzón, A. R. Garzón, R. Pérez +3
Mathematics · #18D05 #18D10 #55P15 #55P48 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.CT #msc:18D05 #msc:18D10 #msc:55P15 #msc:55P48
paper · pdf · doi:10.48550/arxiv.1103.4485
arxiv created 2011/03/23 · openalex publication_date 2011/03/23 · arxiv updated 2011/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Thomason's Homotopy Colimit Theorem has been extended to bicategories and this extension can be adapted, through the delooping principle, to a corresponding theorem for diagrams of monoidal categories. In this version, we show that the homotopy type of the diagram can be also represented by a genuine simplicial set nerve associated with it. This suggests the study of a homotopy colimit theorem, for diagrams \b of braided monoidal categories, by means of a simplicial set \em nerve of the diagram. We prove that it is weak homotopy equivalent to the homotopy colimit of the diagram, of simplicial sets, obtained from composing \b with the geometric nerve functor of braided monoidal categories.