Date of Original Version

3-4-2013

Type

Article

Rights Management

Copyright The Author [2013]. Published by Oxford University Press. The version of record is available online at http://dx.doi.org/10.1093/philmat/nkt030

Abstract or Description

The recent discovery of an interpretation of constructive type theory into abstract homotopy theory suggests a new approach to the foundations of mathematics with intrinsic geometric content and a computational implementation. Voevodsky has proposed such a program, including a new axiom with both geometric and logical significance: the Univalence Axiom. It captures the familiar aspect of informal mathematical practice according to which one can identify isomorphic objects. While it is incompatible with conventional foundations, it is a powerful addition to homotopy type theory. It also gives the new system of foundations a distinctly structural character.

DOI

10.1093/philmat/nkt030

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Philosophy Commons

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Published In

Philosophia Mathematica, 22, 1, 1-11.