Small presentations of model categories and Vopěnka's principle
|Year of publication
|Article in Periodical
|Magazine / Source
|Homology, Homotopy and Applications
|MU Faculty or unit
|cobrantly generated model category; combinatorial model category; simplicial presheaves; Vopěnka's principle
|We prove existence results for small presentations of model categories generalizing a theorem of D. Dugger from combinatorial model categories to more general model categories. Some of these results are shown under the assumption of Vopěnka's principle. Our main theorem applies, in particular, to cofibrantly generated model categories where the domains of the generating cofibrations satisfy a slightly stronger smallness condition. As a consequence, assuming Vopěnka's principle, such a cofibrantly generated model category is Quillen equivalent to a combinatorial model category.