On a Model Invariance Problem in Homotopy Type Theory
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Abstract
In this article, the author endows the functor category [B(Z/2Z),Gpd] with the structure of a type-theoretic fibration category with a univalent universe, using the so-called injective model structure. This gives a new model of Martin-Löf type theory with dependent sums, dependent products, identity types and a univalent universe. This model, together with the model (developed by the author in another work) in the same underlying category and with the same universe, which turns out to be provably not univalent with respect to projective fibrations, provide an example of two Quillen equivalent model categories that host different models of type theory. Thus, we provide a counterexample to the model invariance problem formulated by Michael Shulman.
Description
Keywords
Journal Title
Conference Name
Journal ISSN
1572-9095