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

@article{Doherty2020CubicalMO, title={Cubical models of \$(\infty, 1)\$-categories}, author={Brandon Doherty and Chris Kapulkin and Zachery Lindsey and Christian Sattler}, journal={arXiv: Algebraic Topology}, year={2020} }

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…

## One Citation

### A cubical model for $(\infty, n)$-categories

- Mathematics
- 2020

We propose a new model for the theory of $(\infty,n)$-categories (including the case $n=\infty$) in the category of marked cubical sets with connections, similar in flavor to complicial sets of…

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