- cubical path type in nLab🔍
- cubical type theory in nLab🔍
- path type in nLab🔍
- Wrapping My Head Around Cubical Path Types🔍
- Path types and identity types in dependent type theory🔍
- A Cubical Approach to Synthetic Homotopy Theory in nLab🔍
- A unifying cartesian cubical type theory🔍
- What learning path should one follow to teach oneself type theory?🔍
cubical path type in nLab
1. Idea. Cubical path types are a form of path types in dependent type theory used in cubical type theories. A major difference between cubical ...
Cubical type theory is a flavor of dependent type theory in which maps out of an interval primitive is used to define cubical path types.
In cubical type theory, the cubical path type path A ( x , y ) \mathrm{path}_A(x, y) for type A A and elements x : A x:A and y : A y:A - this is ...
Wrapping My Head Around Cubical Path Types - Shea Levy
Cubical type theory is a computational interpretation of Voevodsky's homotopy type theory based on a cubical set model.
nForum - cubical path type - nLab
The rules for path types currently do not include any coercion or composition rules. Do the path types actually behave like paths/identity types without ...
Path types and identity types in dependent type theory - MathOverflow
Unlike Martin-Lof identity types, cubical path types really are "paths" in the sense of "function out of an interval", although the interval is ...
A Cubical Approach to Synthetic Homotopy Theory in nLab
Path-over-a-path types and higher generalizations are used to describe cubes in a fibration over a cube in the base. These higher-dimensional ...
A unifying cartesian cubical type theory - Google Groups
type formers of cubical type theory (nat, Sigma, Pi, Path, Id, Glue, U) ... DeMorgan cubical sets. https://ncatlab.org/nlab/show/cubical+type+theory#models.
What learning path should one follow to teach oneself type theory?
HoTT / cubical agda / nlab are probably not good places to start, the first two are very specialized and nlab is much more of a reference than a ...
Identity types in cubical type theory are called path types and are defined using a primitive interval. 6. Categorical semantics. We discuss the ...
cubical-type model category in nLab
These exist a class of model category structures on certain categories of cubical sets, due to Christian Sattler, motivated by cubical type ...
Three non-cubical applications of extension types - arXiv
The development of cubical type theory inspired the idea of “extension types” which has been found to have applications in other type theories that are ...
A type theory for synthetic ∞-categories - Emily Riehl
stracted over using “extension types” that generalize the path-types of cubical type theory. ... Draft available at https://ncatlab.org/ · nlab/files/ ...
Categorification and the Cosmic Cube | The n-Category Café
This should certainly find its way to nLab: univalence axiom. The Idea section there seems to promote the path/bundle aspects at the moment. As ...
'homotopy-type-theory' tag wiki - Proof Assistants Stack Exchange
... type theory – which takes seriously the natural interpretation of identity types as formalizing path space objects in homotopy theory. (from nLab). References:
The natural home for the semantics of typed predicate logic turns out to be an indexed poset: a category C C together with a functor P : C op → ...
The key idea behind cubical type theory, and thus our implementation Cubical Agda, is that by axiomatizing the important properties of [0,1] as an interval type ...
Using Agda to Explore Path-Oriented Models of Type Theory
models of type theory? A Search nLab [Urs Schreiber]. For things like nLab ... Ian Orton & AMP, Axioms for Modelling Cubical Type Theory in a. Topos. In ...
Homotopy Type Theory should eat itself (but so far, it's too big to ...
In particular, by the recursion principle for higher inductive types, the clauses of these definitions corresponding to the path-constructors ...
Homotopy type theory - Wikipedia
^ Univalence is a type, a property of the identity type IdU of a universe U —Martín Hötzel Escardó (2018) · ^ "Univalence is a type, and the univalence axiom ...