Axioms for Modelling Cubical Type Theory in a Topos

The homotopical approach to intensional type theory views proofs of equality as paths. We explore what is required of an object $I$ in a topos to give such a path-based model of type theory in which paths are just functions with domain $I$. Cohen, Coquand, Huber and M\"ortberg give such a model...

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Bibliographic Details
Main Authors: Ian Orton, Andrew M. Pitts
Format: Article
Language:English
Published: Logical Methods in Computer Science e.V. 2018-12-01
Series:Logical Methods in Computer Science
Subjects:
Online Access:https://lmcs.episciences.org/4491/pdf