Homotopy Theory for Ordered Simplicial Complexes
arXiv:2509.22968
Abstract
We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a new model for the homotopy theory of spaces.
v3, fixed the adjunction establishing the Quillen equivalence in Section 4