[PDF] 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, ...

Lecture Notes on Cubical sets

A prime example of a de Morgan algebra, which is not a Boolean algebra, is the interval [0, 1] with max(i, j), min(i, j) operations. We assume a ...

[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 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 ...

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, ...

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,.

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.

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/ ...

THE ROLE OF SYMMETRIES IN CUBICAL SETS AND CUBICAL ...

Abstract. Symmetric weak cubical categories were introduced in [G3, G5], as a basis for the study of cubical cospans and higher cobordism. Such.

Higher order automata, cubical sets, and some conjectures of ...

Example: W∞ = class of all functors C → D such that. BC → BD is a weak equiv. of simplicial sets. Conjecture 1: W∞ is the smallest weak equivalence class.

Choice, Collection and Covering in Cubical Sets

E.g. In constructive set theory it is used to show the class of ... Note that we constructed pα to have the following properties: I Setting ...

A Unifying Cartesian Cubical Set Model

Univalent Type Theory has a constructive model in De Morgan Kan cubical sets (“CCHM model”). We also developed a cubical type theory in which we ...

SIMPLICIAL SETS INSIDE CUBICAL SETS 1. Introduction - tac.mta.ca

Writing F for the class of fibrations in cSet the class of Kan fibrations in sSet is given ... pdf. [GS17]. N. Gambino and C. Sattler, The ...

cartesian cubical model categories - Steve Awodey

Of course, some early work like the original papers of D. Kan [Kan55, Kan56] employed cubical sets, and some researchers such as R. Brown [Bro18] ...

Unifying Cubical Models of Univalent Type Theory - Evan Cavallo

An important feature of cubical sets, relative to simplicial sets, is that the product of representable cubical ... In Lecture Notes in Computer Science, pages ...

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.

A Cubical Language for Bishop Sets

Saint-Donat, Lecture Notes in Mathematics, Vol. 269, 270, 305 ... URL: https://www2.mathematik.tu-darmstadt.de/~streicher/NOTES/lift.pdf.

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 ...

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 ...

The Cubical Model of Type Theory - Fachbereich Mathematik

... Lecture notes, http: · //www.mathematik.tu-darmstadt.de/~streicher/FIBR/natmod.pdf. [Str14b]. , A Model of Type Theory in Simplicial Sets: A ...