Publication Date:
2014-02-16
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.
Print ISSN:
0031-8019
Electronic ISSN:
1744-6406
Topics:
Mathematics
,
Philosophy
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