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The Equivalence Extension Property and Model Structures

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arxiv 1704.06911 v4 pith:REZME7ID submitted 2017-04-23 math.CT math.ATmath.LO

Christian Sattler This is my paper · ORCID
classification math.CTmath.ATmath.LO
keywords modelcertainconstructionsetsstructuresargumentclasscohen
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We give an elementary construction of a certain class of model structures. In particular, we rederive the Kan model structure on simplicial sets without the use of topological spaces, minimal complexes, or any concrete model of fibrant replacement such as Kan's Ex^infinity functor. Our argument makes crucial use of the glueing construction developed by Cohen et al. in the specific setting of certain cubical sets.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Extension Types for Free

    cs.LO 2026-07 accept novelty 8.0 of 10 full

    Extension types are definable in two-level type theory, all their Riehl–Shulman rules become theorems, and cubical gluing is equivalent to univalence in this framework.

  2. Duality theory for categorical theories

    math.CT 2026-05 unverdicted novelty 6.0 of 10

    Generalizes categorical theories to coherent theories and proves a duality identifying the 2-category of categorical pretopoi with profinite monoids, further realizing the latter as a full sub-2-category of topoi via ...

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