Kripke-Joyal forcing for type theory and uniform fibrations

• Steve Awodey ^[3] ; Nicola Gambino ^[1] ; Sina Hazratpour ^[2]
  1. [1] University of Manchester

     University of Manchester

     Reino Unido

     
  2. [2] Johns Hopkins University

     Johns Hopkins University

     Estados Unidos

     
  3. [3] Departments of Philosophy and Mathematics, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 4, 2024, págs. 1-70
• Idioma: inglés
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• Resumen

  • We introduce a new method for precisely relating algebraic structures in a presheaf category and judgements of its internal type theory. The method provides a systematic way to organise complex diagrammatic reasoning and generalises the well-known Kripke-Joyal forcing for logic. As an application, we prove several properties of algebraic weak factorisation systems considered in Homotopy Type Theory