Homotopy type theory
Homotopy type theory - Wikipedia
Homotopy type theory ... In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type ...
The HoTT Book | Homotopy Type Theory
About the book. NotableBookCR2013. Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It ...
Homotopy Type Theory: What is it? - MathOverflow
An object is a point, a proof of equality is a path, a proof that two proofs of equality are "the same" is a homotopy.
Homotopy type theory is a flavor of type theory – specifically of intensional dependent type theory – which takes seriously the natural ...
Homotopy Type Theory - a summary of what I've learned : r/math
Type theory is a foundation of math, proclaimed as the main competitor to set theory. Unlike in set theory, type theory distinguishes between collections ( ...
This site serves to collect and disseminate research, resources, and tools for the investigation of homotopy type theory, and hosts a blog ...
[2212.11082] Introduction to Homotopy Type Theory - arXiv
This is an introductory textbook to univalent mathematics and homotopy type theory, a mathematical foundation that takes advantage of the structural nature of ...
All homework and exam work is to be solely your own, and may not be shared with or borrowed from any other person in the course.
What is...homotopy type theory? - YouTube
Goal. I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much. This time.
An Introduction to Homotopy Type Theory & Univalent Foundations
Dependent type theory is: • a formal system for mathematical constructions and proofs,. • which can be related to the conventional foundations of mathematics,.
Homotopy Type Theory: Univalent Foundations of Mathematics
We did not set out to write a book. The present work has its origins in our collective attempts to develop a new style of “informal type theory” that can be ...
Homotopy Type Theory, I | The n-Category Café - Welcome
The goal of this project is to develop a formal language and semantics, similar to the language and semantics of set theory, but in which the fundamental ...
Examples of the benefits of Homotopy Type Theory for computer ...
Homotopy Type Theory is proposed as a new foundation of mathematics, and it supposed to be superior for use with computer aided proofs.
homotopy type theory FAQ in nLab
One could add to homotopy type theory the higher inductive type of propositional truncation, which takes any type and turns it into a ...
Homotopy Type Theory - Steve Awodey
Homotopy Type Theory is a new branch of mathematical logic based on a recently discovered connection between topology. (Homotopy theory) and logic (Type ...
What is Homotopy Type Theory Good For? | The n-Category Café
Most research in homotopy type theory revolves around the fine-tuning of the formulation itself and completing the understanding of its relation to traditional ...
Introduction to Homotopy Type Theory | Hacker News
Martin-Löf type theory (and, therefore, homotopy type theory) is like an idealized programming language that is capable of expressing both ...
Homotopy Type Theory: Univalent Foundations of Mathematics - arXiv
Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory.
Teruji Thomas, Homotopy Type Theory and Structuralism - PhilArchive
Homotopy type theory adds to CST a distinctive theory of identity between sets, which arguably allows its objects to be seen as ante rem ...
Higher Groups in Homotopy Type Theory - ACM Digital Library
Abstract. We present a development of the theory of higher groups, including infinity groups and connective spectra, in homotopy type theory. An infinity group ...