Fibrantly generated weak factorization systems (Q6618800)

The principal result in this paper is that, assuming Vopĕnka's principle, every projectivity class in a locally presentable category is accessible and accessibly embedded. It is also shown that the above principal result is equivalent to the fact that every object of a locally presentable category is \(\mu\)-pure injective for some regular cardinal \(\mu\). The relation of fibrantly generated weak factorization systems to cotorsion theories generated by sets is elucidated.