Affiliation:
1. Department of Mathematics Johns Hopkins University Baltimore Maryland USA
Abstract
AbstractMany introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set‐based foundations. This expository article, written as lecture notes to accompany a three‐part mini course delivered at the Logic and Higher Structures workshop at CIRM‐Luminy, attempt to survey the state of the art, first presenting Voevodsky's simplicial model of univalent foundations and then touring Shulman's vast generalization, which provides an interpretation of homotopy type theory with strict univalent universes in any ‐topos. As we will explain, this achievement was the product of a community effort to abstract and streamline the original arguments as well as develop new lines of reasoning.
Funder
Vetenskapsrådet
National Science Foundation
Air Force Office of Scientific Research
Reference57 articles.
1. M.Anel G.Biedermann E.Finster andA.Joyal Left‐exact localizations of∞$\infty$‐Topoi I: higher sheaves arXiv:2101.02791
2. Natural models of homotopy type theory
3. S.Awodey On Hofmann–Streicher universes arXiv:2205.10917 2022.
4. Voevodsky’s Univalence Axiom in Homotopy Type Theory
5. Homotopy theoretic models of identity types
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Modal fracture of higher groups;Differential Geometry and its Applications;2024-10