Model Structures on the Category of Simplicial Sets

Abstract

AbstractIn this chapter we will apply the formalism of Quillen model categories discussed in the previous chapter to the category of simplicial sets. In his first exposition of the theory of model categories, Quillen already showed that the category of simplicial sets carries a model structure for which the fibrant objects are the Kan complexes and the fibrations are the Kan fibrations (see Chapter 5 for a discussion of these notions).