2019/06/21 by Chris Kapulkin, Kapulkin, Chris, Zachery Lindsey +3
Mathematics · #18G55 #55U35 #55U40 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1906.09203
openalex publication_date 2019/06/21 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
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.