Homotopy type theory

¬P do not hold in Type Theory, hence we cannot define ∨ or ∃ via ¬ and ∧ and ∀. Later we will see a refinement of the proposition as types ...

Overview of Homotopy Type Theory and the Univalent Foundations ...

Rooted in type theory, the theoretical basis of most modern proof assistants, the system admits an interpretation as a logical calculus for homotopy theory and ...

Higher Algebra in Homotopy Type Theory - Ulrik Buchholtz

the connection between homotopy theory & Martin-Löf type theory. • Specific type theories: Typically MLTT + Univalence. (+ HITs + Resizing + Optional ...

Homotopy Type Theory Permits 'Logic of Homotopy Types' - Ideas

It is based on a recently discovered connection between homotopy theory and type theory. Homotopy theory is an outgrowth of algebraic topology and homological ...

Does Homotopy Type Theory Provide a Foundation for Mathematics?

Homotopy Type Theory (HoTT) is first and foremost a research programme within mathematics that connects algebraic topology with logic, computer science, and ...

Homotopy Type Theory in Lean - Floris van Doorn

There is also an impressive experimental proof assistant implementing cubical type theory [7] which is designed with the homotopy interpretation in mind, but it ...

HoTT/book: A textbook on informal homotopy type theory - GitHub

Repository files navigation. README. This is a textbook on informal homotopy type theory. It is part of the Univalent foundations of mathematics project that ...

Homotopy Type Theory - Indiana University Mathematics

Homotopy Type Theory is a new development that establishes surprising connections between logic, algebra, geometry, topology, computer science, and physics.

Homotopy Type Theory | SpringerLink

Homotopy Type Theory is a new, homotopical interpretation of constructive type theory. It forms the basis of the recently proposed Univalent Foundations of ...

Homotopy Type Theory (hardcover) - eBay

Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way.

Homotopy Type Theory 2017

But at the same time, type theory can also be seen as a programming language and lies at the basis of proof assistants, such as Agda and Coq. Homotopy type ...

A cubical model of homotopy type theory - ScienceDirect.com

There is a cubical model of basic homotopy type theory in which the identity type of a type A can be taken to be the path-object.

[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 ...

W-types in homotopy type theory | Cambridge Core

Related content · The effective model structure and $\infty $ -groupoid objects · Model Category Theory since Quillen · Simplicial Objects · Monoidal Bousfield ...

What is homotopy type theory? - Quora

Homotopy Type Theory (HoTT) is a variant/extension of Martin-Loef Type Theory that features the univalence axiom and higher inductive types ( ...

(Homotopy) Type Theory: Chapter One - ezyang's blog

The visual intuition for the path induction is that both ends are “free floating”. If you can prove a proposition is true of any reflexive path, ...

Homotopy Type Theory: Univalent Foundations of Mathematics

... homotopy the- ory and type theory. Homotopy theory is an outgrowth of algebraic topology and homological algebra, with relationships to higher category theory ...

Introduction to Homotopy Type Theory - NASA/ADS

This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature ...

Blog | Homotopy Type Theory

The Homotopy Type Theory (HoTT) Game is a project written by mathematicians for mathematicians interested in HoTT and no experience in proof ...

Homotopy type theory: unified foundations of mathematics and ...

Abstract. Homotopy type theory is a recently-developed unification of previously disparate frameworks, which can serve to advance the project of ...