This entry is about the article
Abstract We show that every combinatorial model category can be obtained, up to Quillen equivalence, by localizing a model category of diagrams of simplicial sets. This says that any combinatorial model category can be built up from a category of “generators” and a set of “relations” — that is, any combinatorial model category has a presentation.
This builds on the companion paper
This shows that, up to Quillen equivalence, every combinatorial model category arises as the left Bousfield localization of the global projective model structure on simplicial presheaves , for some small category
Notice (as discussed at the relevant entries) that
every combinatorial model category can be enhanced to a combinatorial simplicial model category;
Under this correspondence, Dugger’s theorem is precisely the model category-theoretic analog of the theorem that every locally presentable (∞,1)-category is a (∞,1)-categorical localization of an (∞,1)-category of (∞,1)-presheaves
This (∞,1)-category theortic interpretation of Dugger’s theorem is proposition A.3.7.6 in