On pseudofunctors sending groups to 2-groups

2021/12/16 by Alan S. Cigoli, Cigoli, Alan S., Sandra Mantovani +3
Mathematics · #18A40 #18C40 #18D30 #18G45 #18M05 #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2112.08695

openalex publication_date 2021/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a category B with finite products, we first characterize pseudofunctors from B to Cat whose corresponding opfibration is cartesian monoidal. Among those, we then characterize the ones which extend to pseudofunctors from internal groups to 2-groups. If B is additive, this is the case precisely when the corresponding opfibration has groupoidal fibres.

Related

• Geometric constructions preserve fibrations
• Local right biadjoints, bistable pseudofunctors and 2-geometries for Grothendieck topoi
• Pseudocolimits of Small Filtered Diagrams of Internal Categories
• Discrete and conservative reflections of fibrations
• Internal 1-topoi in 2-topoi