@inbook{b4b6c8d7714e4dbcb79a3e1042448e7f,
title = "Univalent foundations and the equivalence principle",
abstract = "In this paper, we explore the {\textquoteleft}equivalence principle{\textquoteright} (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 {\textquoteleft}1 ∈ N{\textquoteright} 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.",
author = "Benedikt Ahrens and {Randall North}, Paige",
year = "2019",
month = nov,
day = "12",
doi = "10.1007/978-3-030-15655-8_6",
language = "English",
isbn = "978-3-030-15654-1",
volume = "407",
series = "Synthese Library",
publisher = "Springer",
pages = "137--150",
editor = "{Centrone }, Stefania and Debora Kant and Deniz Sarikaya",
booktitle = "Reflections on the Foundations of Mathematics",
}