Homotopy Type Theory and Computing — Classical and Quantum

Directed univalence in simplicial homotopy type theory

A number of definitions and theorems from classical ∞-category theory have been ported to STT and the proofs are shorter and more conceptual. Even better, ...

Quantum Programming and Verification

... category theory, proof theory or computer science. [15] ... quantum computation, formulated as an embedded language inside of homotopy type theory.

Research – Álvaro Pelayo - Bitácoras de Matemáticas

Homotopy type theory is a recently created field of mathematics which interprets type theory from a homotopical perspective. An introduction to this area may be ...

Homotopy type theory and the formalization of mathematics

In this sense, topos theo- ry subsumes classical set theory. ... of notable items published in computing by Computing Reviews of the Association.

Newest 'homotopy-type-theory' Questions - Page 3 - MathOverflow

The homotopy interpretation of constructive dependent type theory, the univalence axiom, higher inductive types, internal languages of higher toposes, univalent ...

Why Higher Category Theory in Physics? - Comments

Do have a look. It's not black magic. The point is that homotopy in mathematics is exactly the formalization of gauge transformation in physics.

Constructivity in Homotopy Type Theory

type theory has distinctively more features than what is commonly called ... that large parts of quantum mechanics can indeed be carried out in a constructive ...

Homotopy Type Theory | PDF | Teaching Mathematics - Scribd

It summarizes some of the key ideas, including: (1) The homotopy theoretic interpretation of type theory relates type theory to structures in homotopy theory. ( ...

The Seifert–van Kampen Theorem in Homotopy Type Theory - DROPS

One of the more intriguing applications of this theory is synthetic homotopy theory: proving and mechanizing type-theoretic versions of theorems in classical ...

Topological Quantum Gates in Homotopy Type Theory - ACT 2023

This provides an obstacle to developing quantum computers with many qbits, which has lead researchers to search for quantum systems which are topologically ...

Quantum Gauge Field Theory in Cohesive Homotopy Type Theory

Then we indicate how the resulting cohesive homotopy type theory naturally serves as a formal foundation for central concepts in quantum gauge field theory.

Can someone give me an absolute layman explanation to homotopy ...

Homotopy type theory (HoTT) overcomes this problem (or parts of this problem) by adding a single axiom to MLTT, called the "univalence axiom" which can ...

Topological Quantum Gates in Homotopy Type Theory

Despite the evident necessity of topological protection for realizing scalable quantum computers, the conceptual underpinnings of ...

Brouwer's fixed-point theorem in real-cohesive homotopy type theory

In a further refinement called 'real-cohesion,' the shape is determined by continuous maps from the real numbers, as in classical algebraic topology. This ...

A Candidate Geometrical Formalism for the Foundations of ...

In other words, homotopy type theory is a way of endowing type theory (and the foundation of mathematics more generally) with a kind of inbuilt ...

Homotopy Type Theory: Unified Foundations of Mathematics and ...

The aim of this proposal is to enable a tightly knit group of expert researchers in logic, math- ematics, and computer science to pursue a ...

Approaching Type theory and Category Theory as a starting point in ...

It seems that many researchers in Type theory and Category Theory in general, specially in Homotopy Type Theory, see their areas as a good ...

What are the advantages of homotopy type theory over Zermelo ...

Type theory is relatively accessible, although you need a pretty good background in logic to really get into it, but homotopy theory requires ...

Previous Seminars - Homotopy Type Theory at CMU

Binary relations are indispensable in classical mathematics, and higher-dimensional analogues of binary relations promise to occupy an important (and ...

Homotopy Types - Oxford Academic - Oxford University Press

Taken together with the 'univalence axiom' there results a language in which anything that can be said of a type can be said of an equivalent type. This allows ...