A 2-Categorical Analysis of the Tripos-to-Topos Construction

2011/04/14 by Jonas Frey, Frey, Jonas · 2 citations
Mathematics · #03G30 (Primary) 18D05 #18D30 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.CT #msc:03G30 #msc:18D05 #msc:18D30

paper · pdf · doi:10.48550/arxiv.1104.2776

arxiv created 2011/04/14 · openalex publication_date 2011/04/14 · arxiv updated 2011/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterize the tripos-to-topos construction of Hyland, Johnstone and Pitts as a biadjunction in a bicategory enriched category of equipment-like structures. These abstract concepts are necessary to handle the presence of oplax constructs --- the construction is only oplax functorial on certain classes of cartesian functors between triposes. A by-product of our analysis is the decomposition of the tripos-to-topos construction into two steps, the intermediate step being a weakened version of quasitoposes.

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