SIMPLICIAL SETS INSIDE CUBICAL SETS 1. Introduction

Simplicial and Cellular Structures in Algebraic Topology

... in homotopy theory. Let me explain how. 1 From Simplicial Complexes to Simplicial Sets and CW complexes. In an attempt to answer Heegaard's criticism on his ...

Notes on simplicial homotopy theory

... in the context of simplicial sets. Thus, In section 1 we study fibrations, introduced in section. 2.1, and the extremely useful concept of anodyne extension ...

A parametricity-based formalization of semi-simplicial and ... - Hal-Inria

... cubical sets to ν-sets, subsuming the earlier definitions. We start with some introductory material on semi-simplicial and semi-cubical sets.

A co-reflection of cubical sets into simplicial sets with applications to ...

... cubical sets. In particular, our theorem gives a model of the homotopy theory of. (∞,1)-categories in cubical sets. To our knowledge, this ...

Nominal Presentation of Cubical Sets Models of Type Theory - DROPS

One of Bezem,. Coquand and Huber's motivations for considering cubical sets instead of simplicial sets is that they can be made a model of univalence within ...

Cubical Set - Martin Baker - EuclideanSpace

This page discusses a cubical version of simplicial sets. Simplicial sets are described on the page here. diagram. The delta category Δ has: Objects: The ...

A model structure on internal categories in simplicial sets

We also study the homotopy theory of internal presheaves over an internal category. Introduction. Infinity-categories are category-like objects in which one can ...

Rigidification of quasi-categories 1 Introduction - University of Oregon

A necklace is a simplicial set obtained by stringing simplices together in succession. In this section we establish some basic facts about them, as well as ...

A unifying cartesian cubical type theory - Google Groups

fibration to simplicial sets. Thomas PS Thierry insists on constructing models in constructive meta theories like CZF with universes or extensional type theory ...

Category of cubical objects and category of simplicial objects

Note that the vertices of the cube Г are functions a: {1,2,..., n}. {0, 1}. We introduce the following ordering relation ^ in the set of vertices of the cube /" ...

Nonabelian Algebraic Topology – Contents - EMS Press

9.10 Simplicial sets and crossed complexes . . . . . . . . . . . . . . . . 319. 10 Resolutions. 324 ... 13.1 Connections and compositions in cubical sets .

A parametricity-based formalization of semi-simplicial and ... - alphaXiv

... definition of both augmented semi-simplicial and semi-cubical sets, and fully formalize it in Coq.

Homotopy types as homotopy types - Emily Riehl

This last part involves joint work with Steve Awodey, Evan Cavallo, Thierry Coquand, and Christian Sattler. Contents. 1. Simplicial sets as ...

Universes in a Type Theory for Synthetic

Simplicial Sets inside Cubical Sets I. The category sSet of simplicial sets is the category of presheaves on the category of finite ordinals ...

Cellular spanning trees and Laplacians of cubical complexes

... sets. The guiding principle is that directions in cubical complexes are analogous to vertices in simplicial complexes. We first generalize our definitions ...

A model of type theory in cubical sets - Page has been moved

Thus it is a step towards a computational interpretation of Voevodsky's Univalence Axiom. Introduction. In [15], Voevodsky proposes a new axiom ...

A Quick Tour of Basic Concepts in Simplicial Homotopy Theory

Now we put together the previous two ideas: a "simplicial set" is a presheaf on the category of simplices! In other words, it's a contravariant ...

Higher fundamental functors for simplicial sets - Numdam

Combinatorial homotopy for symmetric simplicial sets, in degree 1 ... In the cubical case, one can similarly use the elementary cubical sets. [n] = 2n = {0 ...

Simplicial sets - Topology - SageMath Documentation

In a simplicial set, a simplex either is non-degenerate or is obtained by applying degeneracy maps to a non-degenerate simplex. INPUT: dim – a non-negative ...

General higher dimensional automata Raussen, Martin

[6]) is used in a similar way as a. A-set – as introduced in [20] – for a simplicial set without degeneracies. We use Dn as an abbreviation for the n-cube In. = ...