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arXiv · 2110.14576

Kripke-Joyal forcing for type theory and uniform fibrations

S. Awodey·N. Gambino·S. Hazratpour
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Abstract

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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S. Awodey, N. Gambino, S. Hazratpour. 2024-05-08. Kripke-Joyal forcing for type theory and uniform fibrations. https://arxiv.org/abs/2110.14576

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