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A (2,1)-model structure for conceptual completeness

2022/02/16 by Kristóf Kanalas, Kanalas, Kristóf
Mathematics · Medicine · #Cancer Treatment and Pharmacology #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.CT

paper · pdf · doi:10.48550/arxiv.2202.08212

arXiv admin note: text overlap with arXiv:2104.13239

arxiv created 2022/02/16 · openalex publication_date 2022/02/16 · arxiv updated 2022/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the (2,1)-categorical analogue of the small object argument and give a (2,1)-model structure on the category of small coherent categories, coherent functors and natural isomorphisms. It is induced by a higher dimensional example of a reflective factorisation system, determined by the full subcategory of pretoposes. We prove it to be right proper and the generating trivial cofibrations are described. Whitehead's theorem gives conceptual completeness.

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