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.
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