Decomposing the Univalence Axiom


Type
Conference Object
Change log
Authors
Pitts, AM 
Abstract

This paper investigates Voevodsky's univalence axiom in intensional Martin-Löf type theory. In particular, it looks at how univalence can be derived from simpler axioms. We first present some existing work, collected together from various published and unpublished sources; we then present a new decomposition of the univalence axiom into simpler axioms. We argue that these axioms are easier to verify in certain potential models of univalent type theory, particularly those models based on cubical sets. Finally we show how this decomposition is relevant to an open problem in type theory.

Description
Keywords
dependent type theory, homotopy type theory, univalent type theory, univalence, cubical type theory, cubical sets
Journal Title
LIPIcs : Leibniz International Proceedings in Informatics
Conference Name
23rd International Conference on Types for Proofs and Programs (TYPES 2017), Post-Proceedings Volume
Journal ISSN
1868-8969
Volume Title
104
Publisher
Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
Sponsorship
EPSRC (1641673)
Relationships
Is supplemented by: