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Kripke-Joyal forcing for type theory and uniform fibrations

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arxiv 2110.14576 v2 pith:3XWV7KEK submitted 2021-10-27 math.LO math.CT

S. Awodey , N. Gambino , S. Hazratpour This is my paper · ORCID
classification math.LOmath.CT
keywords theorytypealgebraicforcingkripke-joyalmethodapplicationcategory
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We introduce a new method for precisely relating certain kinds of 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.

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  1. Algebraic Type Theory, Part 1: Martin-L\"of algebras

    math.CT 2025-05 conditional novelty 6.0 of 10

    Introduces Martin-Löf algebras as algebraic models of dependent type theory and constructs a bicategory E//U in which the type former laws become pseudomonoid laws.

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