Homotopy Type Theory : Univalent Foundations of Mathematics (original) (raw)

A Primer on Homotopy Type Theory Part 1: The Formal Type Theory

James Ladyman

2014

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Universes and Univalence in Homotopy Type Theory

James Ladyman

The Review of Symbolic Logic

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On the homotopy types

Thiago Alexandre

2022

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Type theory and homotopy

Steve Awodey

2010

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Foundations of Mathematics: a new proposal based on Homotopy Type Theory

Irene Bosco

Master's Thesis, 2018

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Homotopy Type Theory and the Vertical Unity of Concepts in Mathematics

David Corfield

What is a Mathematical Concept?

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Identity in Homotopy Type Theory, Part I: The Justification of Path Induction

James Ladyman

Philosophia Mathematica, 2015

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Realizability of Homotopy Type Theory

Wouter W P Stekelenburg

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Homotopy theoretic models of identity types

Steve Awodey

2007

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Does Homotopy Type Theory Provide a Foundation for Mathematics?

James Ladyman

The British Journal for the Philosophy of Science, 2016

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The vertical unity of concepts in mathematics through the lens of homotopy type theory

David Corfield

2016

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Modal Homotopy Type Theory

David Corfield

2020

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Identity in Homotopy Type Theory: Part II, The Conceptual and Philosophical Status of Identity in HoTT

James Ladyman

Philosophia Mathematica, 2016

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Modelling and computing homotopy types: I

Ronald Brown

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Semi-simplicial Types in Logic-enriched Homotopy Type Theory

Zhaohui Luo

arXiv (Cornell University), 2015

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Expressing ‘the structure of’ in homotopy type theory

David Corfield

Synthese, 2017

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Group-theoretic algebraic models for homotopy types

Antonio Martinez Cegarra

Journal of Pure and Applied Algebra, 1991

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On the Use of Computational Paths in Path Spaces of Homotopy Type Theory

Arthur Pérez ramos

ArXiv, 2018

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The HoTT library: a formalization of homotopy type theory in Coq

Jason Gross

Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs

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Intuitionistic type theory

Per Martin-Löf

1984

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Overview on Models in Homotopical Algebra

Roberto Ruiz

2004

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Another introduction to Martin-Löf ’ s Intuitionistic Type Theory

Silvio Valentini

2004

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Jeffrey Strom: “Modern Classical Homotopy Theory”

Birgit Richter

Jahresbericht der Deutschen Mathematiker-Vereinigung, 2012

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2-adjoint Equivalences in Homotopy Type Theory

DANIEL RAMOS CARRANZA

Log. Methods Comput. Sci., 2021

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How Intensional Is Homotopy Type Theory?

thomas streicher

Springer eBooks, 2015

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An overview of type theories

Nino Guallart

Axiomathes, 2014

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Meta-mathematical aspects of Martin-Löf's type theory

Silvio Valentini

2000

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CONSTRUCTIVE TYPE THEORY, AN APPETIZER

Laura Crosilla

Higher-Order Metaphysics, 2023

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Copredication in homotopy type theory

Hamidreza Bahramian

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A Cartan–Eilenberg approach to homotopical algebra

Agustí Roig

Journal of Pure and Applied Algebra, 2010

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Naive cubical type theory

Bruno Bentzen

Mathematical Structures in Computer Science, 2022

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Type theories, normal forms, and D∞-lambda-models

Maddalena Zacchi

Information and Computation, 1987

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CORCORAN ON TYPE THEORY—SUBMITTED VERSION

John Corcoran

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A model for the homotopy theory of homotopy theories

Charles Rezk

2012

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A Modern Perspective on Type Theory From its Origins until Today

Twan Laan, HCM de Swart

Journal of Logic, Language and Information, 2006

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