• Corpus ID: 218581869

Cubical models of $(\infty, 1)$-categories

  title={Cubical models of \$(\infty, 1)\$-categories},
  author={Brandon Doherty and Chris Kapulkin and Zachery Lindsey and Christian Sattler},
  journal={arXiv: Algebraic Topology},
We construct a model structure on the category of cubical sets with connections whose cofibrations are the monomorphisms and whose fibrant objects are defined by the right lifting property with respect to inner open boxes, the cubical analogue of inner horns. We show that this model structure is Quillen equivalent to the Joyal model structure on simplicial sets via the triangulation functor. As an application, we show that cubical quasicategories admit a convenient notion of a mapping space… 
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