Homotopy colimits of diagrams over posets and variations on a theorem of Thomason

2014/07/21 by Ximena Fernández, Ximena Fernandez, Fernandez, Ximena +3
Computer Science · Mathematics · #06A06 #18A30 #18B35 #55P15 #55U10 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.AT #math.CO #msc:06A06 #msc:18A30 #msc:18B35 #msc:55P15 #msc:55U10

paper · pdf · doi:10.48550/arxiv.1407.5646

12 pages

arxiv created 2014/07/21 · openalex publication_date 2014/07/21 · arxiv updated 2014/07/23 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We use a classical result of McCord and reduction methods of finite spaces to prove a generalization of Thomason's theorem on homotopy colimits over posets. In particular this allows us to characterize the homotopy colimits of diagrams of simplicial complexes in terms of the Grothendieck construction on the diagrams of their face posets. We also derive analogues of well known results on homotopy colimits in the combinatorial setting, including a cofinality theorem and a generalization of Quillen's Theorem A for posets.

Related

• coCartesian fibrations and homotopy colimits
• A homotopy colimit theorem for diagrams of braided monoidal categories
• Homotopy types of diagrams of chain complexes
• On Quillen's Theorem A for posets
• Homotopy theory of diagrams