model structure on cubical sets in nLab
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 ...
The category of cubical sets admits a Cisinski model structure, which admits a Quillen equivalence to the Kan–Quillen model structure on simplicial sets.
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 ...
cubical set - exposition in nLab
2. Cubical sets in homotopy theory · Eilenberg and Mac Lane proved a normalisation theorem which may be found in Mac Lane's book 'Homology'.
model structure on cubical sets - nForum
Still, it should be useful to have as much cubical homotopy theory around as possible. Many structures are more naturally cubical than simplicial. So as soon as ...
model structure for cubical quasicategories in nLab
The analogue of the Joyal model structure for cubical sets, with or without connections. 2. Related concepts. Joyal model structure, ...
The category of cubes has a concise description in category-theoretic terms but I would rather describe it like this: It's the category in which ...
connection on a cubical set in nLab
As a model for homotopy theory ... The ordinary cube category is a test category. This means that bare cubical sets carry the structure of a ...
A unifying cartesian cubical type theory - Google Groups
A special case of our result is a model structure on cartesian cubical sets that does not require that the diagonal map on the interval is a cofibration (i.e. " ...
Model Structures for ∞-Groupoids and ∞-Categories on Cubical Sets
Model Structures for ∞-Groupoids and ∞-Categories on Cubical Sets. 273 views · 4 years ago ...more. MSRI / SLMath. 2.25K.
model structure on cubical presheaves in nLab
Context · Model category theory · ( ∞ , 1 ) (\infty,1) -Topos Theory.
The equivariant model structure on cartesian cubical sets - arXiv
Abstract:We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy ...
A Perspective on Higher Category Theory | The n-Category Café
... nLab so I can easily look up quasi-category. ... It is known how to use cubical sets to model all weak ∞ \infty -groupoids: this is given by the ...
Cubical stuff - Wiki - Evan Patterson
Although simplicial stuff is the standard for algebraic topology, “cubical stuff”—the cube category , cubical sets , cubical objects in a category, and so on— ...
Cubical type theory can be modeled in a number of varieties of cubical sets, for example in a type-theoretic model structure. 6. Related ...
nLab -- General Discussion | The n-Category Café - Welcome
... cubical sets? Sure! I started now describing the idea a bit more in the section Idea at n n Lab: cubical set. Have a look and let me know if ...
Evan Cavallo, Why some cubical models don't present spaces
... structure was inspired by Kan's early work on cubical sets. However, cubical type theory inteprets in forms of cubical sets not considered ...
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.
From Cubes to Twisted Cubes via Graph Morphisms in Type Theory
Cube categories are used to encode higher-dimensional categorical structures. ... A model of type theory in cubical sets. 19th International ...
arXiv:2406.18497v1 [math.AT] 26 Jun 2024
There is a constructively definable model of HoTT in cartesian cubical sets with an associated constructively definable Quillen model structure ...