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{{Short description|Model structure on the category of simplicial sets}}
In [[higher category theory]] in mathematics, the '''Joyal model structure''' is a special [[model structure]] on the [[category of simplicial sets]]. It consists of three classes of morphisms between simplicial sets called ''fibrations'', ''cofibrations'' and ''weak equivalences'', which fulfill the properties of a model structure. Its fibrant objects are all [[∞-category|∞-categories]] and it furthermore models the [[homotopy theory]] of [[CW complex]]es up to [[homotopy equivalence]], with the correspondence between simplicial sets and CW complexes being given by the [[Geometric realization functor|geometric realization]] and the singular functor. The Joyal model structure is named after [[André Joyal]].
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