Homotopy type theory and Voevodsky's univalent foundations

Homotopy type theory and Voevodsky's univalent foundations - arXiv

In this paper we give an introduction to homotopy type theory in Voevodsky's setting, paying attention to both theoretical and practical issues.

Voevodsky's univalent perspective, as detailed in his Coq files, is a unique view of mathematics, and we believe that it deserves to be more ...

The HoTT Book | Homotopy Type Theory

Homotopy type theory offers a new “univalent” foundation of mathematics, in which a central role is played by Voevodsky's univalence axiom and higher inductive ...

Homotopy Type Theory: Univalent Foundations of Mathematics

... Homotopy type theory also brings new ideas into the very foundation of mathematics. On the one hand, there is Voevodsky's subtle and beautiful univalence ...

Homotopy Type Theory: Univalent Foundations of Mathematics - arXiv

On the one hand, Voevodsky's subtle and beautiful "univalence axiom" implies that isomorphic structures can be identified. On the other hand, " ...

Homotopy type theory and Voevodsky's univalent foundations

This paper serves as an introduction to both the general ideas of homotopy type theory as well as to some of the concrete details of Voevodsky's work using ...

Homotopy Type Theory and Univalent Foundations - andrew.cmu.ed

Homotopy type theory refers to a new interpretation of Martin-Löf's constructive type theory into homotopy theory.

Homotopy Type Theory (hardcover) - Lulu

... Homotopy type theory offers a new “univalent” foundation of mathematics, in which a central role is played by Voevodsky's univalence axiom ...

Homotopy type theory - Wikipedia

There is a large overlap between the work referred to as homotopy type theory, and that called the univalent foundations project. Although neither is precisely ...

An Introduction to Homotopy Type Theory & Univalent Foundations

Voevodsky: “I was sure that we were right until the fall of 2013 (!!)” Page 3. A sociological problem. “A technical argument by a trusted author, which ...

Homotopy Type Theory and Univalent Foundations of Mathematics

The homotopy interpretation suggests new logical constructions and axioms. 5. Voevodsky's Univalent Foundations program combines these aspects into a new ...

nLab Homotopy Type Theory -- Univalent Foundations of Mathematics

... Voevodsky's univalence axiom and higher inductive types. The present book is intended as a first systematic exposition of the basics of ...

Deligne's doubt about Voevodsky's Univalent Foundations

I believe that if we add LEM and AC, the answer is probably still no. There are other "classicality axioms" for synthetic homotopy theory that I ...

Homotopy type theory and univalent foundations

What Voevodsky named the “univalent foundations of mathematics” arose from a recently discovered homotopy theoretic interpretation of dependent type theory ...

Univalent Foundations and the Large-Scale Formalization of ...

Steve Awodey, Alvaro Pelayo, and Michael A. Warren, “Voevodsky's Univalence Axiom in Homotopy Type Theory,” Notices of the American Mathematical Society ( ...

[PDF] Homotopy Type Theory: Univalent Foundations of Mathematics

Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ...

Univalent foundations - Wikipedia

"Homotopy type theory and Voevodsky's univalent foundations". Bulletin of the American Mathematical Society. 51 (4): 597–648. arXiv:1210.5658. doi:10.1090 ...

Homotopy type theory and Voevodsky's univalent foundations

A condition that ensures the existence of the filtration h is [35] : This axiom can be understood as saying that equality expands to cover equivalences. This ...

Univalent Foundations of Mathematics - Vladimir Voevodsky

... homotopy types using Martin-Lof type theories. In this talk I will explain how to define usual mathematical objects starting with homotopy types ...

Special Issue on Homotopy Type Theory and Univalent Foundations

The univalence axiom has originally been justified by Vladimir Voevodsky using the simplicial sets model, but the cubical sets model is the ...