Date of Original Version
Copyright The Author . 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.
Philosophia Mathematica, 22, 1, 1-11.