Kripke-Joyal forcing for type theory and uniform fibrations

Fuente: arXiv
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Bibliographic Details
Main Authors: Awodey, S., Gambino, N., Hazratpour, S.
Format: Preprint
Published: 2021
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author Awodey, S.
Gambino, N.
Hazratpour, S.
author_facet Awodey, S.
Gambino, N.
Hazratpour, S.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2110_14576
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Kripke-Joyal forcing for type theory and uniform fibrations
Awodey, S.
Gambino, N.
Hazratpour, S.
Logic
Category Theory
03G30, 03B38, 18F20, 18N45
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.
title Kripke-Joyal forcing for type theory and uniform fibrations
topic Logic
Category Theory
03G30, 03B38, 18F20, 18N45
url https://arxiv.org/abs/2110.14576