Homotopy Type Theory Permits 'Logic of Homotopy Types'
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 ...
Homotopy Type Theory: Univalent Foundations of Mathematics - arXiv
Abstract:Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type ...
Homotopy Type Theory - Institute for Advanced Study
Homotopy Type Theory Permits 'Logic of Homotopy Types' ... The following text is excerpted from the introduction to the book Homotopy Type Theory: Univalent ...
Homotopy Type Theory: Univalent Foundations of Mathematics
... homotopy type theory, they permit an entirely new kind of “logic of homotopy types”. This suggests a new conception of foundations of mathematics, with ...
Homotopy Type Theory - Steve Awodey
(Homotopy theory) and logic (Type Theory). ▷ Martin-Löf type theory (a ... The rules for identity types permit the inference: p : IdX (a,b) c : F(a) p ...
[2212.11082] Introduction to Homotopy Type Theory : r/math - Reddit
Homotopy type theory is exactly a form of constructive higher order logic with the univalence axiom. As well as being a useful setting for ...
Homotopy type theory - Wikipedia
In mathematical logic and computer science, homotopy type theory (HoTT) refers to various lines of development of intuitionistic type theory, based on the ...
[1201.3898] Inductive types in homotopy type theory - arXiv
There results a link between constructive mathematics and algebraic topology, providing topological semantics for intensional systems of type ...
Homotopy Type Theory: a new foundation for 21st-century ...
Homotopy type theory unifies type theory, arising from logic and computer science, with homotopy theory, which talks about topological spaces.
Homotopy Type Theory, I | The n-Category Café - Welcome
Roughly, the goal of this project is to develop a formal language and semantics, similar to the language and semantics of set theory, but in ...
... homotopy type theory, they permit an entirely new kind of “logic of homotopy types ”. This suggests a new conception of foundations of ...
The HoTT Book | Homotopy Type Theory
Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way.
In what sense does Homotopy type theory "model types as spaces"
Just to add a little bit to the answers below, since you've emphasized the textbook definition of structures in first-order logic, the models ...
In homotopy type theory, the fundamental objects are types, which seamlessly play the role of both spaces and logical propositions. The axioms of these types ...
homotopy type theory FAQ in nLab
Traditional set theory is formulated in first-order logic. Under the propositions as types interpretation, first order logic maps soundly and ...
The homotopy theory of type theories - ScienceDirect.com
This allows a precise formulation of the conjectures that intensional type theory gives internal languages for higher categories, and provides a ...
A Primer on Homotopy Type Theory Part 1 - PhilSci-Archive
the 'Propositions as Types' approach, which allows a constructive logic to be in- corporated into the basic structure of the type theory itself, ...
Homotopy Type Theory and Univalent Foundations of Mathematics
▻ once as logical objects: types are “propositions” and their terms are “proofs”, which are being derived. Page 18. Propositions as Types. The system has a ...
Homotopy Type Theory - PKC - Obsidian Publish
Overall, Homotopy Type Theory aims to bridge the gap between logic, mathematics, and computer science by providing a unified framework for ...
3 Homotopy Type Theory: A Synthetic Approach to Higher Equalities
Homotopy type theory and univalent foundations (HoTT/UF) is a new foundation of mathematics, based not on set theory but on “infinity-groupoids”, ...