Lecture Notes on Cubical sets
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, ...
The interval I is the cubical set defined by I(J) = dM(J). This defines a functor since any map. I → dM(J) corresponds exactly to a de Morgan ...
[PDF] Lecture Notes on Cubical sets - Semantic Scholar
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, ...
Cubical Sets · To each object c c c in , a set X ( c ) X(c) X(c). Since the objects of are all [ n ] [n] [n], these are alternatively notated ...
cubical sets and their site - marco grandis and luca mauri - tac.mta.ca
Note also that in the theory of involutive symmetric cubical monoids ... spaces, Lecture Notes in Mathematics vol. 347, Springer 1973. [3] R. Brown ...
arXiv:1812.07600v1 [math.AT] 18 Dec 2018
In this note we study the singular homology groups of cubical sets with connections. We were originally motivated by computational ...
Syntax and Models of Cartesian Cubical Type Theory
a broader class of mathematical models, including not only Cartesian cubical sets, but ... Notes on cubical sets. Available from https://github.com/awodey/math/ ...
SIMPLICIAL SETS INSIDE CUBICAL SETS 1. Introduction - tac.mta.ca
Key words and phrases: cubical sets, simplicial sets, universes, univalence axiom. ... Writing F for the class of fibrations in cSet the class of ...
A Model of Type Theory in Cubical Sets - DROPS
Note that the unit interval is not the cubical nerve of the poset 0 ... Calculi and Applications, number 664 in Lecture Notes in Computer Science, 1993.
cubical approach to straightening - Mathematics
They were considered by Kan. [Kan55, Kan56] before the introduction of simplicial sets. ... Reyes, First order categorical logic, Lecture Notes in ...
cubical set - exposition in nLab
2. Cubical sets in homotopy theory · normalization of chains is essential · cubical groups are not automatically fibrant · the geometric ...
cubical-approach-to-straightening.pdf
They were considered by Kan. [Kan55, Kan56] before the introduction of simplicial sets. ... des schemas I, II, III, Lecture Notes in Mathematics, vol. 269, 270, ...
Note that ep+1(x#y) = (ep+1x)#y = x#(e1y) is well defined precisely because of the previous equivalence relation. The identity of the tensor product is the ...
Introduction to Cubical Sets - YouTube
Dr. Chris Kapulkin University of Western Ontario.
Cubical sets as a classifying topos
[Coq15] Thierry Coquand. Lecture notes on cubical sets. 2015. [Doc14] Simon Docherty. A model of type theory in cubical sets with connections. Master's thesis,.
A hands-on introduction to cubicaltt - Homotopy Type Theory
Cubical Type Theory has a model in cubical sets with lots of structure (symmetries, connections, diagonals) and is hence consistent. Furthermore ...
Nominal Presentation of Cubical Sets Models of Type Theory - DROPS
in the theory of nominal sets [15, Chapter 2]. However, it generalizes ... and Programs, volume 1158 of Lecture Notes in Computer Science, pages 120–134.
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 ...
cartesian cubical model categories - Steve Awodey
The second source for Cartesian cubical sets is F.W. Lawvere, who proposed them as a model for homotopy theory in lectures, and in public and ...
arXiv:1612.08485v2 [math.PR] 19 Mar 2018
In Section 2, after brief introduction of cubical sets and cubical ... wide class of random cubical sets. We continue to use notation ...