cubical|type model category in nLab
cubical-type model category in nLab
A class of model category structures on certain categories of cubical sets, due to Christian Sattler, motivated by cubical type theory.
Univalent cubical type theory models the ∞ \infty -groupoid-structure implied by Martin-Löf identity types on constructive cubical sets (whence ...
model structure on cubical sets in nLab
Using this version of the homotopy hypothesis-theorem, cubical sets are a way to describe the homotopy type of ∞-groupoids using of all the ...
A cubical ∞-category is a cubical set equipped with operations giving a way to compose cubes with each other, in the same way that an ordinary ∞ ...
The category of cubical sets admits a Cisinski model structure, which admits a Quillen equivalence to the Kan–Quillen model structure on simplicial sets.
For starters, it is a category equipped with three classes of morphisms, each closed under composition and called weak equivalences, fibrations ...
Cubical path types are a form of path types in dependent type theory used in cubical type theories.
Can everything in category theory be restated in a sufficiently ...
Thus a category can be interpreted as an "abstract data structure" and functors between categories are just ordinary (type theoretic) functions ...
Is there a shape-independent definition of (∞,1)-categories?
In the case of Simplicial Type Theory, baking in theory of cubes at the cube layer. This brings me to my question: Is there a definition of (∞,1) ...
The Mysterious Nature of Right Properness | The n-Category Café
The type-theoretic “model structure” also has the property that all objects are fibrant and cofibrant. But once you're willing to relax the ...
What are the motivations for different variants of categorical models ...
Structures that are more "categorical", arising naturally from categories "in nature" without the need for strictification theorems. In ...
model structure on cubical presheaves in nLab
nLab model structure on cubical presheaves · Contents. 1. Idea; 2. Related concepts; 3. References. 1. Idea.
A unifying cartesian cubical type theory - Google Groups
We hence obtain the Sattler model structure on De Morgan and distributive lattice cubical sets as a special case when the cube category has connections.
Stable homotopy type theory? - hopf algebras - MathOverflow
Heuristically, the starting point is the fact that in any category C with (Cartesian) products every object X has a unique comonoid structure, ...
Homotopy Type Theory, III | The n-Category Café
The other triangle identity then follows; see the nLab page. I didn't really say anything about why these types should be equivalent, though.
In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak ...
The nLab - the (n-)category as a "grand narrative" in mathematics ...
"Higher category theory studies the generalization of ∞-groupoids – and hence, via the homotopy hypothesis, of topological spaces – to that of ...
From Cubes to Twisted Cubes via Graph Morphisms in Type Theory
The higher categories encoded with the BCH cube category have the property that all morphisms are invertible, mirroring the fact that equality ...
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 ...
category of cubes - exposition in nLab
The cube category is used to define cubical sets. ... Hence cubical sets model homotopy types (see also model structure on cubical sets).