The paper is devoted to some generalizations of projectivity classes, weakly coreflexive categories and cotorsion theories from the category of \(R\)-modules to arbitrary locally presentable categories. If \(\mathcal K\) is a finitely presented category and \(\mathcal A\) is a weakly coreflexive full subcategory of \(\mathcal K\) which is closed under directed colimits in \(\mathcal K\), then \(\mathcal A\) is stably weakly coreflective. If \((\mathcal F,\mathcal C)\) is a cotorsion theory in the category \(R\)-\(mod\) such that \(\mathcal F\) is closed under directed colimits, then (\(\mathcal F\)-Mono, \(\mathcal C\)-Epi) is a stable weak factorization system.