- Semantics of higher inductive types🔍
- Jon Sterling🔍
- Syllepsis in Homotopy Type Theory🔍
- Homotopy Type Theory 🔍
- Categorical homotopy theory Emily Riehl🔍
- A survey of constructive models of univalence🔍
- The Functor of Points Approach to Schemes in Cubical Agda🔍
- Univalent Foundations of Constructive Algebraic ...🔍
A Cubical Approach to Synthetic Homotopy Theory in nLab
Semantics of higher inductive types | Cambridge Core
... homotopy-theoretic constructions in a type-theoretic style. They have proven very fruitful for the “synthetic” development of homotopy theory ...
It is based on a recently discovered connection between homotopy theory and type theory. It touches on topics as seemingly distant as the homotopy groups of ...
Syllepsis in Homotopy Type Theory
Figure 3. The periodic table of 𝑛-categories, as updated by Baez and Shulman [2010] and seen on the nLab. k n.
Homotopy Type Theory (HoTT) for Mere Mortals | by Haliq | Medium
In a flip of perspective due to the homotopy interpretation, type theorists are now studying structures from category theory such as toposes to ...
Categorical homotopy theory Emily Riehl - Personal pages
The viewpoint taken by William Thurston's essay—that mathematical progress is made by advancing human understanding of mathematics and not ...
A survey of constructive models of univalence
See Categorical Homotopy Theory, Riehl, Theorem 15.3.1 or nlab. Hence we get a new class of complete Cisinski model structures. 40. Page 42. A ...
Re: [HoTT] Formalization of π₄(S³)≅ℤ/2ℤ in Cubical Agda ...
Discussion of Homotopy Type Theory and Univalent Foundations · help / color / mirror / Atom feed. From: Anders Mortberg
The Functor of Points Approach to Schemes in Cubical Agda - DROPS
Keywords and phrases Schemes, Algebraic Geometry, Category Theory, Cubical Agda, Homotopy. Type Theory and Univalent Foundations, Constructive Mathematics.
Univalent Foundations of Constructive Algebraic ... - DiVA portal
for “higher” mathematics and synthetic homotopy theory. ... lattice described in [ZM23] adopts this approach ... theory that can be formalized in a proof assistant ...
Johns Hopkins Category Theory Seminar
Our approach is crucially based on Licata-Riley-Shulman's fibrational framework for modal type theories. Furthermore, we suggest a notion of synthetic co-/ ...
A cubical model of homotopy type theory. Annals of Pure and Applied Logic ... synthetic homotopy theory, CMU, Pure and Applied Logic, 2018. pdf. Egbert ...
Cubical Type Theory – Synthetic
Cubical Models of (∞, 1)-Categories. Brandon Doherty, Chris Kapulkin, Zachery Lindsey, Christian Sattler. 2022. Parametricity and Semi-Cubical Types. Hugo ...
Relation Between Type Theory, Category Theory and Logic
Homotopy type theory (HoTT) overcomes this problem (or parts of this problem) by adding a single axiom to MLTT, called the "univalence axiom" ...
dmarx/nlab_feb24 · Datasets at Hugging Face
... theory]] and [[homotopy theory]]. \begin{lemma} If $C$ is [[presentable (infinity,1)-category|presented]] by a [[simplicial model category]] $A$, in that $C ...
From the nLab to the HoTT Book - Sandiego
3 Choose appropriate project structure. 4 Embrace synthetic mathematics. Page 4. The nLab. Homotopy type theory. The ...
A Cubical Approach to Synthetic Homotopy Theory - Semantic Scholar
A cubical approach to developing homotopy theory within type theory by isolating higher-dimensional cube types as independent conceptual abstractions has ...
Hypercubes in cubical type theory : r/dependent_types - Reddit
Cubical/homotopy type theory has another way of structuring this. The restrictions in the previous approaches were necessary to maintain the idea that the ...
Homotopy type theory is the internal language of higher toposes. I can only read the sentence as a prediction and a prescription but it is ...
This is a consequence of the univalence axiom: any property or structure (even one which speaks only about sets and makes no reference to ...
Dominic Verity: "Zen and the art of ∞-categories" - YouTube
... theory with a little homotopy theory thrown in”. Inspired by that comment, you might even have headed to a book on ∞-categories or to the nLab ...