Cubical Sets
1. Definition. Notation 1.1. We make use of the notation of category of cubes. Definition 1.2. The category of cubical sets is the free co- ...
Cubical set ... In topology, a branch of mathematics, a cubical set is a set-valued contravariant functor on the category of (various) n-cubes. Cubical sets have ...
It's the category in which the objects are all powers of the set of booleans, { 0 , 1 } n \{0,1\}^n {0,1}n, which we abbreviate to [ n ] [n]
cubical set - exposition in nLab
A cubical set is a space characterized by the fact that, and the ways in which, it may be probed by mapping standard cellular cubes into it.
These are some lecture notes for a course presenting the cubical set model of type theory, first in. Copenhagen, December 2014, and then in Paris, ...
Introduction to Cubical Sets - YouTube
Dr. Chris Kapulkin University of Western Ontario.
[1701.08189] Varieties of Cubical Sets - arXiv
We define a variety of notions of cubical sets, based on sites organized using substructural algebraic theories presenting PRO(P)s or Lawvere theories.
Cubical sets and their site - tac.mta.ca
Extended cubical sets (with connections and interchanges) are presheaves on a ground category, the extended cubical site K, corresponding to the (augmented) ...
What is the intuition of connections for cubical sets? - MathOverflow
The extra structure of connections brings cubical sets nearer to simplicial sets, but keeping other advantages, such as easily understood definitions of ...
Category of cubical sets : r/askmath - Reddit
For the first definition of the category of cartesian cubes, what are interval objects? The only thing I've been able to find is this. It seems ...
Nominal Presentation of Cubical Sets Models of Type Theory - DROPS
The cubical sets model of Homotopy Type Theory introduced by Bezem, Coquand and Huber [2] uses a particular category of presheaves. We show that this presheaf ...
cubical sets and their site - marco grandis and luca mauri - tac.mta.ca
Extended cubical sets (with connections and interchanges) are presheaves on a ground category, the extended cubical site K, corresponding to the (augmented).
[PDF] Varieties of Cubical Sets - Semantic Scholar
This work defines a variety of notions of cubical sets, based on sites organized using substructural algebraic theories presenting PRO(P)s or Lawvere ...
Cubical Sets and Trace Monoid Actions - PMC
This paper is devoted to connections between trace monoids and cubical sets. We prove that the category of trace monoids is isomorphic to the category of ...
The equivariant model structure on cartesian cubical sets - arXiv
We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces.
Andrew Swan, Why cubical sets are different to simplicial sets
Homotopy Type Theory Electronic Seminar Talks, 2022-01-20 https://www.uwo.ca/math/faculty/kapulkin/seminars/hottest.html In the classical ...
Simplicial set are to cubical sets what simplicial complexes are to
Simplicial sets and cubical sets (with or without connections) are defined as presheaves over some indexing categories. There is a full ...
cubical-approach-to-straightening.pdf
The category cSet of cubical sets is the category of contravariant functors Dop → Set and natural transformations. We will write Dn for the standard n-cube, ...
Cubical sets and their site. - EuDML
Grandis, Marco, and Mauri, Luca. "Cubical sets and their site.." Theory and Applications of Categories [electronic only] 11 (2003): 185-211.
Cubical stuff - Wiki - Evan Patterson
Cubical stuff. Although simplicial stuff is the standard for algebraic topology, “cubical stuff”—the cube category , cubical sets , cubical objects in a ...