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

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.

arXiv comment12 pages

References in corpus (2)

• A necessary and sufficient condition for induced model structures
• Lifting accessible model structures