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A simplicial set is said to be non-singular if its non-degenerate simplicesare embedded. Let $sSet$ denote the category of simplicial sets. We prove thatthe full subcategory $nsSet$ whose objects are the non-singular simplicial setsadmits a model structure such that $nsSet$ becomes is Quillen equivalent to$sSet$ equipped with the standard model structure due to Quillen. The modelstructure on $nsSet$ is right-induced from $sSet$ and it makes $nsSet$ a propercofibrantly generated model category. Together with Thomason's model structureon small categories (1980) and Raptis' model structure on posets (2010) theseform a square-shaped diagram of Quillen equivalent model categories in whichthe subsquare of right adjoints commutes.

Homotopy Theory of Non-singular Simplicial Sets