Univalent foundations and the equivalence principle

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)


Colleges, School and Institutes

External organisations

  • Ohio State University


In this paper, we explore the ‘equivalence principle’ (EP): roughly, statements about mathematical objects should be invariant under an appropriate notion of equivalence for the kinds of objects under consideration. In set theoretic foundations, EP may not always hold: for instance, the statement ‘1 ∈ N’ is not invariant under isomorphism of sets. In univalent foundations, on the other hand, EP has been proven for many mathematical structures. We first give an overview of earlier attempts at designing foundations that satisfy EP. We then describe how univalent foundations validates EP.


Original languageEnglish
Title of host publicationReflections on the Foundations of Mathematics
EditorsStefania Centrone , Debora Kant, Deniz Sarikaya
Publication statusE-pub ahead of print - 12 Nov 2019

Publication series

NameSynthese Library