Abstract. We give an elementary construction of a certain class of model structures. In particular, we rederive the Kan model structure on simplicial sets without the use of topological spaces, minimal complexes, or any concrete model of fibrant replacement such as Kan's Ex ∞ functor. Our argument makes crucial use of the glueing construction developed by Cohen et al. [CCHM16] in the specific setting of certain cubical sets.
In particular, clarify the connection of the model structure on cubical sets REF and the usual model structure on simplicial sets.
The Equivalence Extension Property and Model Structures
arXiv: Category Theory
Mathematics