English

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

Category Theory 2019-06-24 v1 Algebraic Topology

Abstract

We show that the category of simplicial sets is a co-reflective subcategory of the category of cubical sets with connections, with the inclusion given by a version of the straightening functor. We show that using the co-reflector, one can transfer any cofibrantly generated model structure in which cofibrations are monomorphisms to cubical sets, thus obtaining cubical analogues of the Quillen and Joyal model structures.

Keywords

Cite

@article{arxiv.1906.09203,
  title  = {A co-reflection of cubical sets into simplicial sets with applications to model structures},
  author = {Chris Kapulkin and Zachery Lindsey and Liang Ze Wong},
  journal= {arXiv preprint arXiv:1906.09203},
  year   = {2019}
}

Comments

12 pages

R2 v1 2026-06-23T10:00:06.151Z