类型理论和均匀纤维的克里普克-乔亚尔强制力

Selecta Mathematica Pub Date : 2024-07-31 DOI:10.1007/s00029-024-00962-2

Steve Awodey, Nicola Gambino, Sina Hazratpour

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引用次数: 0

摘要

我们引入了一种新方法，用于精确地将预设范畴中的代数结构与其内部类型理论的判断联系起来。这种方法为组织复杂的图解推理提供了一种系统化的方式，并概括了著名的克里普克-乔亚尔（Kripke-Joyal）逻辑强制法。作为应用，我们证明了同调类型理论中考虑的代数弱因式分解系统的几个性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Kripke-Joyal forcing for type theory and uniform fibrations

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Kripke-Joyal forcing for type theory and uniform fibrations

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.

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Selecta Mathematica

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