Thomason's colimit theorem for the double category of elements

2025/06/09 by Gill, Andrew, Maru Sarazola, Sarazola, Maru
Mathematics · #18D30 #18N10 #55P15 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2506.08246

openalex publication_date 2025/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that, for any 2-category C and 2-functor F\colon C → Cat, the double category of elements \iint_C F introduced by Grandis and Paré satisfies a version of Thomason's colimit theorem; that is, there is a weak homotopy equivalence B hocolim F≃ B(\iint_C F).

Citations

• Internal Grothendieck construction for enriched categories
• Bi-initial objects and bi-representations are not so different
• 2-limits and 2-terminal objects are too different
• 2-Dimensional Categories
• Homotopy colimits of 2-functors
• Fibred 2-categories and bicategories
• Homotopy Fibre Sequences Induced by 2-Functors

Related

• Homotopy colimits of 2-functors
• Homotopy Fibre Sequences Induced by 2-Functors
• Higher Equipments, Double Colimits and Homotopy Colimits
• On the equvialence of colimits and 2-colimits
• Thomason cohomology and Quillen's Theorem A